document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1093704>Question 1093704</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The focal chord that cuts the parabola x^2= -6y at (6, -6) and cuts the parabola again at X. Find the coordinates of X. \r<BR>\n" );
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document.write( "I tried to solve it...what am I doing wrong:<BR>\n" );
document.write( "concave down<BR>\n" );
document.write( "-4a=-6<BR>\n" );
document.write( "a= -3/2<BR>\n" );
document.write( "vertex at (0,0) <BR>\n" );
document.write( "so, focus is at (0,3/2)\r<BR>\n" );
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document.write( "I used the 2 point formula y - y1 = m(x - x1) and found the gradient of (6,-6) and (0,3/2): <BR>\n" );
document.write( "m= -4/3<BR>\n" );
document.write( "y-6=-4/3 (x+6)<BR>\n" );
document.write( "y=-4/3x+14\r<BR>\n" );
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document.write( "used simultaneous equations x^2= -6y and y=-4/3x+14 to find the intersection points but did not get the right answer.. is my process right?<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 #708328 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=708328\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> any chord that passes through the Parabola's focus point is a focal cord<BR>\n" );
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document.write( "x^2 = -6y<BR>\n" );
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document.write( "we are given one intersection point of the focal cord, namely (6, -6)<BR>\n" );
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document.write( "the center is at (0,0)<BR>\n" );
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document.write( "4p = -6<BR>\n" );
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document.write( "p = -6/4 = -3/2 = -1.5<BR>\n" );
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document.write( "the focus is -1.5 units from y coordinate of the center, namely (0, -1.5)<BR>\n" );
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document.write( "we have two points on the cord, (6, -6) and (0, -1.5)<BR>\n" );
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document.write( "slope = (-1.5 -(-6)) / (0 -6) = 4.5 / -6 = -0.75 = -3/4<BR>\n" );
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document.write( "y = -3x/4 +b<BR>\n" );
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document.write( "use point (6, -6) to find b<BR>\n" );
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document.write( "-6 = -3(6)/4 + b<BR>\n" );
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document.write( "-24 = -18 +4b<BR>\n" );
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document.write( "4b = -6<BR>\n" );
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document.write( "b = -6/4 = -1.5<BR>\n" );
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document.write( "y = -3x/4 -1.5<BR>\n" );
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document.write( "-3x/4 -1.5 = -x^2/6<BR>\n" );
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document.write( "-9x -18 = -2x^2<BR>\n" );
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document.write( "2x^2 -9x -18 = 0<BR>\n" );
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document.write( "(2x+3) * (x-6) = 0<BR>\n" );
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document.write( "x = -3/2 and x = 6<BR>\n" );
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document.write( "we choose x = -1.5 then<BR>\n" );
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document.write( "y = -3(-1.5)/4 -1.5 = 1.125 -1.5 = &#8722;0.375<BR>\n" );
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document.write( "coordinates of X are (-1.5, -0.375)<BR>\n" );
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