document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1087652>Question 1087652</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the equation<BR>\n" );
document.write( "of the parabola<BR>\n" );
document.write( "whose focus is (1,<BR>\n" );
document.write( "–2) and directrix is<BR>\n" );
document.write( "the line parallel to<BR>\n" );
document.write( "6x – 7y + 9 = 0<BR>\n" );
document.write( "and directrix<BR>\n" );
document.write( "passes through<BR>\n" );
document.write( "point (3/2,2) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #701970 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=701970\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  Solution:\r<BR>\n" );
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document.write( "Let (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" >) be any point on the parabola. Then by definition, the distance between (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" >) and the focus (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-2 ALIGN=MIDDLE  ALT=\"+-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >) must be equal to the length of perpendicular from (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" >) on directrix. \r<BR>\n" );
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document.write( "So first we will find the equation of the directrix.\r<BR>\n" );
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document.write( "The line parallel to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x+-7y+%2B+9+=+0 ALIGN=MIDDLE  ALT=\"6x+-7y+%2B+9+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > …… (1)\r<BR>\n" );
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document.write( "Since directrix passes through (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F2 ALIGN=MIDDLE  ALT=\"3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" >), this point will satisfy equation (1) and hence \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%283%2F2%29+-7%282%29+%2B+k+=+0 ALIGN=MIDDLE  ALT=\"6%283%2F2%29+-7%282%29+%2B+k+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k+=+-9+%2B+14 ALIGN=MIDDLE  ALT=\"k+=+-9+%2B+14\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k+=+5 ALIGN=MIDDLE  ALT=\"k+=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " Equation of directrix is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x+-7y+%2B+5+=+0 ALIGN=MIDDLE  ALT=\"6x+-7y+%2B+5+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " Now by definition of parabola,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%28x+-1%29%5E2+%2B+%28y+%2B2%29%5E2%29+=+%286x-7y+%2B+5%29%2Fsqrt%286%5E2+%2B+7%5E2%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >...square both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%28%28x+-1%29%5E2+%2B+%28y+%2B2%29%5E2%29+%29%5E2=+%286x-7y+%2B+5%29%5E2%2F%28sqrt%2885%29%29%5E2 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+85%28%28x+-+1%29%5E2+%2B+%28y+%2B+2%29%5E2%29+=+%286x+-7y+%2B+5%29%5E2 ALIGN=MIDDLE  ALT=\"+85%28%28x+-+1%29%5E2+%2B+%28y+%2B+2%29%5E2%29+=+%286x+-7y+%2B+5%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=49x%5E2+%2B+36y%5E2+%2B+84xy+-230x+%2B+410y+%2B+400+=0 ALIGN=MIDDLE  ALT=\"49x%5E2+%2B+36y%5E2+%2B+84xy+-230x+%2B+410y+%2B+400+=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >-> your equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C%0D%0Acircle%281%2C-2%2C.12%29%2C+locate%281%2C-2%2CF%281%2C-2%29%29%2C%0D%0Acircle%283%2F2%2C2%2C.12%29%2C+locate%283%2F2%2C2%2Cp%283%2F2%2C2%29%29%2C+%0D%0Alocate%283%2C4%2Cdirectrix%286x+-7y+%2B+5+%29%29%2C%0D%0A+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C%281%2F36%29%28-42x-5sqrt%2885%29sqrt%2812x%2B13%29-205%29%2C%281%2F36%29%28-42x%2B5sqrt%2885%29sqrt%2812x%2B13%29-205%29%2C6x%2F7%2B+5%2F7%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
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