document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=576205>Question 576205</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please show me how to solve this....\r<BR>\n" );
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document.write( "1.)How high is a parabolic arc pf span 24m and height 18m at distance 8 from the center of it span?\r<BR>\n" );
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document.write( "2.)A chord passing through the focus of the parabola x^2=16y has one end  at pt. (12,9). Where is the end of the other chord?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #369896 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=369896\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1.) Let's make x the horizontal distance (in m) from the center of the span (which would be right below the vertex of the parabola, the top of the arch).<BR>\n" );
document.write( "Let's make y, the height, in meters.<BR>\n" );
document.write( "The top of the arch would be the (0,18), the vertex of the parabola.<BR>\n" );
document.write( "For all x between -12 and 12,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=ax%5E2%2B18 ALIGN=MIDDLE  ALT=\"y=ax%5E2%2B18\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "That is the equation of the parabola in vertex form (because the vertex is (0,18).<BR>\n" );
document.write( "We just need to find a, knowing that for x=12, and x=-12, y=0.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=a%2A12%5E2%2B18 ALIGN=MIDDLE  ALT=\"0=a%2A12%5E2%2B18\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=144a%2B18 ALIGN=MIDDLE  ALT=\"0=144a%2B18\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=144a=-18 ALIGN=MIDDLE  ALT=\"144a=-18\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=-18%2F144 ALIGN=MIDDLE  ALT=\"a=-18%2F144\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=-1%2F8 ALIGN=MIDDLE  ALT=\"a=-1%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-x%5E2%2F8%2B18 ALIGN=MIDDLE  ALT=\"y=-x%5E2%2F8%2B18\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "I am going to assume that is the problem means to ask how high is the arc above a point on the ground that is 8 m from the center of the span.<BR>\n" );
document.write( "At 8 meters from the center of the span, on the ground, x=8.<BR>\n" );
document.write( "At that point,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-8%5E2%2F8%2B18=-8%2B18=10 ALIGN=MIDDLE  ALT=\"y=-8%5E2%2F8%2B18=-8%2B18=10\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "2.) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2=16y ALIGN=MIDDLE  ALT=\"x%5E2=16y\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The axis of symmetry is x=0, the y axis, because y has the same value for x and -x.<BR>\n" );
document.write( "The vertex of the parabola is the point (0,0) on thay axis of symmetry.<BR>\n" );
document.write( "The focus of the parabola will be a point (0,c), and the directrix will be the line x=-c.<BR>\n" );
document.write( "The point of the parabola with y=c, is at a (vertically measured) distance 2c from horizontal directrix x=-c. By the definition of parabola, the (horizontally measured) distance from that point to focus (0,c) is the same 2c, so for x=2c, y=c, and substituting into the equation for thee parabola, we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282c%29%5E2=16c ALIGN=MIDDLE  ALT=\"%282c%29%5E2=16c\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4c%5E2=16c ALIGN=MIDDLE  ALT=\"4c%5E2=16c\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=4 ALIGN=MIDDLE  ALT=\"c=4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So the focus is at (0,4).<BR>\n" );
document.write( "The chord that passes through the focus and through (12,9) has a slope of<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=slope=%289-4%29%2F%2812-0%29=5%2F12 ALIGN=MIDDLE  ALT=\"slope=%289-4%29%2F%2812-0%29=5%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so its equation is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=5x%2F12%2B4 ALIGN=MIDDLE  ALT=\"y=5x%2F12%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" > since its y-intercept is the focus (0,4).<BR>\n" );
document.write( "The intersection points of that line and the parabola <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2=16y ALIGN=MIDDLE  ALT=\"x%5E2=16y\"   DISABLED_style= \"max-width:90%; height:auto;\" > will be solutions of<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2=16%285x%2F12%2B4%29 ALIGN=MIDDLE  ALT=\"x%5E2=16%285x%2F12%2B4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2=20x%2F3%2B64 ALIGN=MIDDLE  ALT=\"x%5E2=20x%2F3%2B64\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> (((3x^2=20x+192}}} --> (((3x^2-20x-192=0}}}<BR>\n" );
document.write( "The quadratic formula says that<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-%28-20%29+%2B-+sqrt%28%28-20%29%5E2-4%2A3%2A%28192%29+%29%29%2F%282%2A3%29=%2820+%2B-+sqrt%28400%2B2304%29%29%2F6=%2820+%2B-+sqrt%282704%29%29%2F6=%2820+%2B-+52%29%2F6 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So the solutions are:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=72%2F6=12 ALIGN=MIDDLE  ALT=\"x=72%2F6=12\"   DISABLED_style= \"max-width:90%; height:auto;\" > (for the point (12,9) given), and for the point we need<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-32%2F6 ALIGN=MIDDLE  ALT=\"x=-32%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=-16%2F3%29 ALIGN=MIDDLE  ALT=\"highlight%28x=-16%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, which corresponds to<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%285%2F12%29%28-16%2F3%29%2B4=-20%2F9%2B4=-20%2F9%2B36%2F9 ALIGN=MIDDLE  ALT=\"y=%285%2F12%29%28-16%2F3%29%2B4=-20%2F9%2B4=-20%2F9%2B36%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28y=16%2F9%29 ALIGN=MIDDLE  ALT=\"highlight%28y=16%2F9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The other end of the chord is at (-16/3,16/9) (unless I made a mistake in the calculations, of course). </SPAN>\n" );
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