document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1128278>Question 1128278</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find the equation satisfied by the set of points such that each is equidistant from (2,-1) and 3x+y-7=0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #744859 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=744859\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> find the equation satisfied by the set of points such that each is equidistant from P(2,-1) and 3x+y-7=0<BR>\n" );
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document.write( "It's a parabola.  The focus is (2,-1) and the directrix is 3x+y-7 = 0<BR>\n" );
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document.write( "Find the equation of the axis of the parabola, the line thru (2,-1) and perpendicular to (call it L1) 3x+y-7=0.<BR>\n" );
document.write( "Slope of L1 = -3<BR>\n" );
document.write( "Slope of perpendicular line = 1/3<BR>\n" );
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document.write( "y+1= (1/3)*(x-2)<BR>\n" );
document.write( "The intersection of the 2 lines is D(13/5,-4/5)<BR>\n" );
document.write( "The midpoint of PD is M(23/10,-9/10), a point on the parabola.<BR>\n" );
document.write( "The distance from M to the line L1 is MD = PM = <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%2823%2F10-2%29%5E2+%2B+%28-1+-+9%2F10%29%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%28%2823%2F10-2%29%5E2+%2B+%28-1+-+9%2F10%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%289%2F100+%2B+1%2F100%29+=+sqrt%2810%29%2F10 ALIGN=MIDDLE  ALT=\"sqrt%289%2F100+%2B+1%2F100%29+=+sqrt%2810%29%2F10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The distance from a point (m,n) to a line Ax + By + C = 0 is:<BR>\n" );
document.write( "(Am + Bn + C)/sqrt(A^2 + B^2)<BR>\n" );
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document.write( "The distance from P to the line L is:<BR>\n" );
document.write( "|2*3 -1*1 -7|/sqrt(9+1) = 2/sqrt(10)<BR>\n" );
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document.write( "Line L2 parallel to L1 thru (2,-1) is y+1 = -3(x-2)<BR>\n" );
document.write( "The 2 points on L2 at a distance of sqrt(10)/10 from P are Q(2.1,-1.3) and <BR>\n" );
document.write( "R(1.9,-0.7)<BR>\n" );
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document.write( "Find the parabola thru the 3 points about the axis.<BR>\n" );
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document.write( "More later.<BR>\n" );
document.write( "My Excel sheet always finds a parabola with its axis parallel to the y-axis.<BR>\n" );
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document.write( "Use this method:<BR>\n" );
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document.write( "For any point (x,y) the distance to (2,-1) is sqrt((x-2)^2 + (y+1)^2)<BR>\n" );
document.write( "The distance to the line L1 is |3x + y - 7|/sqrt(10)<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5E2+=+%28x-2%29%5E2+%2B+%28y%2B1%29%5E2+=+%283x%2By-7%29%5E2%2F10 ALIGN=MIDDLE  ALT=\"d%5E2+=+%28x-2%29%5E2+%2B+%28y%2B1%29%5E2+=+%283x%2By-7%29%5E2%2F10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%2A%28x%5E2-4x%2B4+%2B+y%5E2%2B2y%2B1%29+=+9x%5E2-42x%2B6xy%2By%5E2-14y%2B49 ALIGN=MIDDLE  ALT=\"10%2A%28x%5E2-4x%2B4+%2B+y%5E2%2B2y%2B1%29+=+9x%5E2-42x%2B6xy%2By%5E2-14y%2B49\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10x%5E2+-+40x+%2B+40+%2B+10y%5E2+%2B+20y+%2B+10+=+9x%5E2-42x%2B6xy%2By%5E2-14y%2B49 ALIGN=MIDDLE  ALT=\"10x%5E2+-+40x+%2B+40+%2B+10y%5E2+%2B+20y+%2B+10+=+9x%5E2-42x%2B6xy%2By%5E2-14y%2B49\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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