document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=864960>Question 864960</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I previously asked this question and got this solution (after question). But I would appreciate further clarification.<BR>\n" );
document.write( "The line with the equation y=mx is tangent to the circle with centre (-8,0) and radius 4 at the point P(x,y). <BR>\n" );
document.write( "a)find x coordinate of P in terms of m <BR>\n" );
document.write( "b)Show that m = +- sqrt (3)/ 3 and hence find the coordinates of P<BR>\n" );
document.write( "(x+8)^2+y^2=16<BR>\n" );
document.write( "(x+8)^2+y^2=16, y=mx<BR>\n" );
document.write( "m = 1/sqrt(3),   x = -6,   y = m x<BR>\n" );
document.write( "m =-1/sqrt(3),   x = -6,   y = m x<BR>\n" );
document.write( "+-1/sqrt(3)=+-sqrt(3)x/3<BR>\n" );
document.write( "y=+-sqrt(3)x/3<BR>\n" );
document.write( "x=-6,   y =2sqrt(3)<BR>\n" );
document.write( "P=(-6,2sqrt(3))<BR>\n" );
document.write( "Can you please provide further clarification- <BR>\n" );
document.write( "Step 3 and 4-<BR>\n" );
document.write( "m = 1/sqrt(3), x = -6, y = m x <BR>\n" );
document.write( "m =-1/sqrt(3), x = -6, y = m x <BR>\n" );
document.write( "How was the x coordinate found. <BR>\n" );
document.write( "Step 5 <BR>\n" );
document.write( "+-1/sqrt(3)=+-sqrt(3)x/3 <BR>\n" );
document.write( "what is happening here for one to become the other.\r<BR>\n" );
document.write( "\n" );
document.write( "I need this explained very simply So i i can understand it. Especially my queries about the steps. Thank you very much.\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #521431 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=521431\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I see several ways to get the answer. I cannot tell if one of the ways I would use was used in the first answer you got. Maybe the reasoning was through a different way. I can explain one or more ways. However, I am a long-winded explainer, so you may get more explanation that you bargained for.<BR>\n" );
document.write( " <BR>\n" );
document.write( "USING GEOMETRY AND ANALYTIC GEOMETRY:<BR>\n" );
document.write( "The tangent to a circle is perpendicular to the radius at the point of tangency, so I would draw the sketch like this:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28600%2C300%2C-15%2C5%2C-5%2C5%2C%0D%0Agrid%280%29%2Cblue%28circle%28-8%2C0%2C4%29%29%2C%0D%0Agreen%28line%28-15%2C8.66%2C5%2C-2.887%29%29%2C%0D%0Agreen%28line%28-15%2C-8.66%2C5%2C2.887%29%29%2C%0D%0Ablue%28circle%28-8%2C0%2C0.1%29%29%2C%0D%0Ablue%28circle%28-8%2C0%2C0.15%29%29%2C%0D%0Agreen%28circle%28-6%2C3.464%2C0.1%29%29%2C%0D%0Ablue%28triangle%28-8%2C0%2C0%2C0%2C-6%2C3.464%29%29%2C%0D%0Ablue%28triangle%28-8%2C0%2C0%2C0%2C-6%2C-3.464%29%29%2C%0D%0Alocate%28-8.15%2C0.6%2CC%29%2Clocate%28-6%2C4%2CP%29%2C%0D%0Alocate%28-7%2C1.9%2C4%29%2Clocate%28-1.3%2C0.6%2Cgreen%28theta%29%29%2C%0D%0Agreen%28arc%280%2C0%2C3%2C3%2C-180%2C-150%29%29%2Clocate%281%2C0.6%2Cgreen%28theta%29%29%2C%0D%0Agreen%28arc%280%2C0%2C3%2C3%2C-30%2C0%29%29%0D%0Alocate%280.1%2C0.6%2CO%29%2Clocate%28-6%2C-3.46%2CQ%29%2C%0D%0Agreen%28line%28-6%2C0%2C-6%2C3.464%29%29%2C%0D%0Alocate%28-5.9%2C2%2Cgreen%28y%29%29%2C%0D%0Agreen%28line%28-6.15%2C3.204%2C-5.89%2C3.054%29%29%2C%0D%0Agreen%28line%28-5.74%2C3.314%2C-5.89%2C3.054%29%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > The tangents, radii, and the x-axis form right triangles OPC and OQC.<BR>\n" );
document.write( "The two triangles are congruent, with P(x,y) and Q(x,-y), so I only need to solve OPC.<BR>\n" );
document.write( "I know that the length of leg CP is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and the hypotenuse OC is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8 ALIGN=MIDDLE  ALT=\"8\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28theta%29=4%2F8=1%2F2 ALIGN=MIDDLE  ALT=\"sin%28theta%29=4%2F8=1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "That tells me that the angle <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=theta ALIGN=MIDDLE  ALT=\"theta\"   DISABLED_style= \"max-width:90%; height:auto;\" > measures <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30%5Eo ALIGN=MIDDLE  ALT=\"30%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and OPC is a 30-60-90 triangle.<BR>\n" );
document.write( "From the tangent of that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30%5Eo ALIGN=MIDDLE  ALT=\"30%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > angle you can also get the slopes of the tangents.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%2830%5Eo%29=1%2Fsqrt%283%29=%281%2Fsqrt%283%29%29%2A%28sqrt%283%29%2Fsqrt%283%29%29=sqrt%283%29%2F%28sqrt%283%29%29%5E2=sqrt%283%29%2F3 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "We multiply times <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%283%29%2Fsqrt%283%29%29 ALIGN=MIDDLE  ALT=\"%28sqrt%283%29%2Fsqrt%283%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > because we do not like to see square roots in denominators,<BR>\n" );
document.write( "so m = +- <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%283%29%2F3 ALIGN=MIDDLE  ALT=\"sqrt%283%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Of course, OP is the line with the negative slope, and OQ is the line with the positive slope.<BR>\n" );
document.write( "For OP, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-sqrt%283%29%2Fsqrt%283%29%29%29x ALIGN=MIDDLE  ALT=\"y=%28-sqrt%283%29%2Fsqrt%283%29%29%29x\"   DISABLED_style= \"max-width:90%; height:auto;\" > and<BR>\n" );
document.write( "for OQ, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28sqrt%283%29%2Fsqrt%283%29%29%29x ALIGN=MIDDLE  ALT=\"y=%28sqrt%283%29%2Fsqrt%283%29%29%29x\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "The altitude of that right triangle splits it into two similar right triangles, CPM, and OPM.<BR>\n" );
document.write( "As the ratio of short leg to hypotenuse for OPC is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F8=1%2F2 ALIGN=MIDDLE  ALT=\"4%2F8=1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the ratio is also the same for CPM, and OPM, so<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=CM=4%2A%281%2F2%29=2 ALIGN=MIDDLE  ALT=\"CM=4%2A%281%2F2%29=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the x-coordinate of points M and P (and Q) is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-8%2B2=highlight%28-6%29 ALIGN=MIDDLE  ALT=\"-8%2B2=highlight%28-6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "For OP, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-sqrt%283%29%2Fsqrt%283%29%29%29x ALIGN=MIDDLE  ALT=\"y=%28-sqrt%283%29%2Fsqrt%283%29%29%29x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and for P, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=mx=m%2A%28-6%29=%28sqrt%283%29%2Fsqrt%283%29%29%2A%28-6%29=2sqrt%283%29 ALIGN=MIDDLE  ALT=\"y=mx=m%2A%28-6%29=%28sqrt%283%29%2Fsqrt%283%29%29%2A%28-6%29=2sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "On the other hand, for Q, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-2sqrt%283%29 ALIGN=MIDDLE  ALT=\"y=-2sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( " <BR>\n" );
document.write( "WITHOUT MENTIONING GEOMETRY (too much):<BR>\n" );
document.write( "OK, we need to know the equation of the circle, and I could call that analytical geometry, but you learn that in algebra 2 too.<BR>\n" );
document.write( "The equation of a circle with radius <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r ALIGN=MIDDLE  ALT=\"r\"   DISABLED_style= \"max-width:90%; height:auto;\" > and center at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22%28+h+%2C+k+%29%22 ALIGN=MIDDLE  ALT=\"%22%28+h+%2C+k+%29%22\"   DISABLED_style= \"max-width:90%; height:auto;\" > is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-h%29%5E2%2B%28y-k%29%5E2=r%5E2 ALIGN=MIDDLE  ALT=\"%28x-h%29%5E2%2B%28y-k%29%5E2=r%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "For the circle in your problem, that would be<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-%28-8%29%29%5E2%2B%28y-0%29%5E2=4%5E2 ALIGN=MIDDLE  ALT=\"%28x-%28-8%29%29%5E2%2B%28y-0%29%5E2=4%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > ---> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B8%29%5E2%2By%5E2=16 ALIGN=MIDDLE  ALT=\"%28x%2B8%29%5E2%2By%5E2=16\"   DISABLED_style= \"max-width:90%; height:auto;\" > ---> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B16x%2B64%2By%5E2=16 ALIGN=MIDDLE  ALT=\"x%5E2%2B16x%2B64%2By%5E2=16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=mx ALIGN=MIDDLE  ALT=\"y=mx\"   DISABLED_style= \"max-width:90%; height:auto;\" > is tangent to the circle, there is only one point in common to circle and line,<BR>\n" );
document.write( "so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28x%5E2%2B16x%2B64%2By%5E2=16%2Cy=mx%29 ALIGN=MIDDLE  ALT=\"system%28x%5E2%2B16x%2B64%2By%5E2=16%2Cy=mx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > has one and only one solution.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28x%5E2%2B16x%2B64%2By%5E2=16%2Cy=mx%29 ALIGN=MIDDLE  ALT=\"system%28x%5E2%2B16x%2B64%2By%5E2=16%2Cy=mx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B16x%2B64%2B%28mx%29%5E2=16 ALIGN=MIDDLE  ALT=\"x%5E2%2B16x%2B64%2B%28mx%29%5E2=16\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B16x%2B64%2Bm%5E2x%5E2=16 ALIGN=MIDDLE  ALT=\"x%5E2%2B16x%2B64%2Bm%5E2x%5E2=16\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28m%2B1%29x%5E2%2B16x%2B64-16=0 ALIGN=MIDDLE  ALT=\"%28m%2B1%29x%5E2%2B16x%2B64-16=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28m%2B1%29x%5E2%2B16x%2B48=0 ALIGN=MIDDLE  ALT=\"%28m%2B1%29x%5E2%2B16x%2B48=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "For what value of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m ALIGN=MIDDLE  ALT=\"m\"   DISABLED_style= \"max-width:90%; height:auto;\" > would that quadratic equation have one and only one solution?<BR>\n" );
document.write( "A quadratic <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2Bbx%2Bc=0 ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > has one and only one real solution when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac=0 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "and then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-b%2F2a ALIGN=MIDDLE  ALT=\"x=-b%2F2a\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "In the case of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28m%2B1%29x%5E2%2B16x%2B48=0 ALIGN=MIDDLE  ALT=\"%28m%2B1%29x%5E2%2B16x%2B48=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=16 ALIGN=MIDDLE  ALT=\"b=16\"   DISABLED_style= \"max-width:90%; height:auto;\" > , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=m%5E2%2B1 ALIGN=MIDDLE  ALT=\"a=m%5E2%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > , and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=48 ALIGN=MIDDLE  ALT=\"c=48\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "It will have one and only one real solution when<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16%5E2-4%2A%28m%5E2%2B1%29%2A48=0 ALIGN=MIDDLE  ALT=\"16%5E2-4%2A%28m%5E2%2B1%29%2A48=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16%5E2=4%2A48%2A%28m%5E2%2B1%29 ALIGN=MIDDLE  ALT=\"16%5E2=4%2A48%2A%28m%5E2%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16%2A16=4%2A3%2A16%2A%28m%5E2%2B1%29 ALIGN=MIDDLE  ALT=\"16%2A16=4%2A3%2A16%2A%28m%5E2%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16%2Across%2816%29=4%2A3%2Across%2816%29%2A%28m%5E2%2B1%29 ALIGN=MIDDLE  ALT=\"16%2Across%2816%29=4%2A3%2Across%2816%29%2A%28m%5E2%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16=12%28m%5E2%2B1%29 ALIGN=MIDDLE  ALT=\"16=12%28m%5E2%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%5E2%2B1=16%2F12 ALIGN=MIDDLE  ALT=\"m%5E2%2B1=16%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%5E2%2B1=4%2F3 ALIGN=MIDDLE  ALT=\"m%5E2%2B1=4%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%5E2=4%2F3-1 ALIGN=MIDDLE  ALT=\"m%5E2=4%2F3-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%5E2=1%2F3 ALIGN=MIDDLE  ALT=\"m%5E2=1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "m = +-<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%281%2F3%29 ALIGN=MIDDLE  ALT=\"sqrt%281%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >= +- <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fsqrt%283%29 ALIGN=MIDDLE  ALT=\"1%2Fsqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >= +- <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%283%29%2F3 ALIGN=MIDDLE  ALT=\"sqrt%283%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "In either case, we can use <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-b%2F2a ALIGN=MIDDLE  ALT=\"x=-b%2F2a\"   DISABLED_style= \"max-width:90%; height:auto;\" > to find the same <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > value:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%5E2%2B1=4%2F3 ALIGN=MIDDLE  ALT=\"m%5E2%2B1=4%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=%28-16%29%2F%28m%5E2%2B1%29%29 ALIGN=MIDDLE  ALT=\"highlight%28x=%28-16%29%2F%28m%5E2%2B1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "That is the \"x coordinate of P in terms of m\" as your problem asked for.<BR>\n" );
document.write( "Maybe this is the way your teacher/book expected you to solve the problem.<BR>\n" );
document.write( "We can calculate further (apparently not required by your problem):<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-16%2F%28%284%2F3%29%29=-16%2A%283%2F4%29=-6 ALIGN=MIDDLE  ALT=\"x=-16%2F%28%284%2F3%29%29=-16%2A%283%2F4%29=-6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );