document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=203604>Question 203604</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please someone help me about this  : <BR>\n" );
document.write( "Find the point of the intersection of the line y=x+2 and the circle (x-1)^2 + y^2=16<BR>\n" );
document.write( "I guess i should find a point on the line which has distance 4 unit from the centre of the circle that is (1,o) but i don't know how!  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #153629 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=153629\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Your problem:<BR>\n" );
document.write( "Find the point of the intersection of the line y=x+2 and the circle (x-1)^2 + y^2=16<BR>\n" );
document.write( "I guess i should find a point on the line which has distance 4 unit from the centre of the circle that is (1,o) but i don't know how! <BR>\n" );
document.write( "-----<BR>\n" );
document.write( "It looks like you have 2 equations to deal with.<BR>\n" );
document.write( "Equation 1 is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+x%2B2 ALIGN=MIDDLE  ALT=\"y+=+x%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Equation 2 is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-1%29%5E2+%2B+y%5E2+=+16 ALIGN=MIDDLE  ALT=\"%28x-1%29%5E2+%2B+y%5E2+=+16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----<BR>\n" );
document.write( "In order to find the points of intersection, you need to find the values of x and y that satisfy both equations simultaneously.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "A relatively simple way to do this is to take the value of y in equation 1 and substitute it for the value of y in equation 2.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "equation 1 says that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+x%2B2 ALIGN=MIDDLE  ALT=\"y+=+x%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "equation 2 says that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-1%29%5E2+%2B+y%5E2+=+16 ALIGN=MIDDLE  ALT=\"%28x-1%29%5E2+%2B+y%5E2+=+16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "if you substitute (x+2) for y in equation 2, you get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-1%29%5E2+%2B+%28x%2B2%29%5E2+=+16 ALIGN=MIDDLE  ALT=\"%28x-1%29%5E2+%2B+%28x%2B2%29%5E2+=+16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----<BR>\n" );
document.write( "now you have one equation in one unknown that can be solved for x.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-1%29%5E2+=+x%5E2+-+2%2Ax+%2B+1 ALIGN=MIDDLE  ALT=\"%28x-1%29%5E2+=+x%5E2+-+2%2Ax+%2B+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > and since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B2%29%5E2+=+x%5E2+%2B+4%2Ax+%2B+4 ALIGN=MIDDLE  ALT=\"%28x%2B2%29%5E2+=+x%5E2+%2B+4%2Ax+%2B+4\"   DISABLED_style= \"max-width:90%; height:auto;\" > you substitute in equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-1%29%5E2+%2B+%28x%2B2%29%5E2+=+16 ALIGN=MIDDLE  ALT=\"%28x-1%29%5E2+%2B+%28x%2B2%29%5E2+=+16\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2+-+2x+%2B+1%29+%2B+%28x%5E2+%2B+4x+%2B+4%29+=+16 ALIGN=MIDDLE  ALT=\"%28x%5E2+-+2x+%2B+1%29+%2B+%28x%5E2+%2B+4x+%2B+4%29+=+16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "when you combine like terms on the left side of this equation, you get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2+%2B+2x+%2B+5+=+16 ALIGN=MIDDLE  ALT=\"2x%5E2+%2B+2x+%2B+5+=+16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----<BR>\n" );
document.write( "you can solve this by completing the square.<BR>\n" );
document.write( "You could also solve this by using the quadratic formula.<BR>\n" );
document.write( "We'll be solving it by completing the square.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "if you divide both sides of this equation by 2, you get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+x+%2B+5%2F2+=+16%2F2 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+x+%2B+5%2F2+=+16%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----<BR>\n" );
document.write( "if you subtract 5/2 from both sides of this equation, you get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+x+=+11%2F2 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+x+=+11%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----<BR>\n" );
document.write( "take ½ the b term which is the coefficient of x which is 1 and you get ½.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "Your squaring factor on the left side of the equation will be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B%281%2F2%29%29%5E2 ALIGN=MIDDLE  ALT=\"%28x%2B%281%2F2%29%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----<BR>\n" );
document.write( "when you multiply this squaring factor out you get:<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+%2B+%281%2F2%29%29%5E2+=+x%5E2+%2B+x+%2B+%281%2F4%29 ALIGN=MIDDLE  ALT=\"%28x+%2B+%281%2F2%29%29%5E2+=+x%5E2+%2B+x+%2B+%281%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----<BR>\n" );
document.write( "since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+%2B+%281%2F2%29%29%5E2+=+x%5E2+%2B+x+%2B+%281%2F4%29 ALIGN=MIDDLE  ALT=\"%28x+%2B+%281%2F2%29%29%5E2+=+x%5E2+%2B+x+%2B+%281%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > then:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+%2B+%281%2F2%29%29%5E2+-+%281%2F4%29+=++x%5E2+%2B+x ALIGN=MIDDLE  ALT=\"%28x+%2B+%281%2F2%29%29%5E2+-+%281%2F4%29+=++x%5E2+%2B+x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----<BR>\n" );
document.write( "Your equation had already become:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+x+=+%2811%2F2%29 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+x+=+%2811%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "which can now become:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B%281%2F2%29%29%5E2+-+%281%2F4%29+=+%2811%2F2%29 ALIGN=MIDDLE  ALT=\"%28x%2B%281%2F2%29%29%5E2+-+%281%2F4%29+=+%2811%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "because <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2+%2B+x%29 ALIGN=MIDDLE  ALT=\"%28x%5E2+%2B+x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x%2B%281%2F2%29%29%5E2+-+%281%2F4%29%29 ALIGN=MIDDLE  ALT=\"%28%28x%2B%281%2F2%29%29%5E2+-+%281%2F4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > are equivalent.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "your equation has now become:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B%281%2F2%29%29%5E2+-+%281%2F4%29+=+11%2F2 ALIGN=MIDDLE  ALT=\"%28x%2B%281%2F2%29%29%5E2+-+%281%2F4%29+=+11%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "If you add (1/4) to both sides of this equation, you get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B%281%2F2%29%29%5E2+=+11%2F2+%2B+%281%2F4%29+=+%2823%2F4%29 ALIGN=MIDDLE  ALT=\"%28x%2B%281%2F2%29%29%5E2+=+11%2F2+%2B+%281%2F4%29+=+%2823%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----<BR>\n" );
document.write( "if you take the square root of both sides of this equation, you get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B%281%2F2%29%29 ALIGN=MIDDLE  ALT=\"%28x%2B%281%2F2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = +/- <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2823%2F4%29 ALIGN=MIDDLE  ALT=\"sqrt%2823%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "if you subtract (1/2) from both sides of this equation, you get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-%281%2F2%29 ALIGN=MIDDLE  ALT=\"x+=+-%281%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > +/- <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2823%2F4%29 ALIGN=MIDDLE  ALT=\"sqrt%2823%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "which makes x =:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%281%2F2%29+%2B+sqrt%2823%2F4%29 ALIGN=MIDDLE  ALT=\"-%281%2F2%29+%2B+sqrt%2823%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%281%2F2%29+-+sqrt%2823%2F4%29 ALIGN=MIDDLE  ALT=\"-%281%2F2%29+-+sqrt%2823%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----<BR>\n" );
document.write( "This becomes:<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "x = -2.8979<BR>\n" );
document.write( "or<BR>\n" );
document.write( "x = +1.8979<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "We can use these values of x to solve for y.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "The equation of:<BR>\n" );
document.write( "(x-1)^2 + y^2 = 16<BR>\n" );
document.write( "becomes:<BR>\n" );
document.write( "y = +/- <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2815-x%5E2%2B2x%29 ALIGN=MIDDLE  ALT=\"sqrt%2815-x%5E2%2B2x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----<BR>\n" );
document.write( "This equation can also be used to graph the problem which will be shown below after all the algebra has been taken care of.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "if x = -2.8979, then y = +/- .897915762<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "if x = 1.8979 then y = +/- 3.8979<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "Of these possible values for y:<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "y = -0.8979 satisfies both equations when x = -2.8979<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "y = + 3.8979 satisfied both equations when x = +1.8979<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "These look like your points of intersection of the line with the circle.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "The intersection points are represented by the ordered pair (x,y)<BR>\n" );
document.write( "One point of intersection is (-2.8979,-0.8979)<BR>\n" );
document.write( "The other point of intersection is (1.8979,3.8979)\r<BR>\n" );
document.write( "\n" );
document.write( "A graph of the equation of the circle and a graph of the equation of the line are shown below and confirm the algebra.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28600%2C600%2C-5%2C5%2C-4%2C4%2Csqrt%2815-x%5E2%2B2%2Ax%29%2C-sqrt%2815-x%5E2%2B2%2Ax%29%2Cx%2B2%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );