document.write( "Question 512206: Compute the focal length and the length of the latus rectum of the parabola y^2 + 8x - 6y + 25 = 0. \n" ); document.write( "
Algebra.Com's Answer #343263 by lwsshak3(11628)\"\" \"About 
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Compute the focal length and the length of the latus rectum of the parabola y^2 + 8x - 6y + 25 = 0.
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\n" ); document.write( "y^2+8x-6y+25=0
\n" ); document.write( "complete the square
\n" ); document.write( "(y^2-6y+9)+8x+25-9=0
\n" ); document.write( "(y-3)^2+8x+16=0
\n" ); document.write( "(y-3)^2+8(x+2)=0
\n" ); document.write( "(y-3)^2=-8(x+2)
\n" ); document.write( "this is an equation of a parabola of standard form: (y-k)^2=-4p(x-h)^2, with (h,k) being the (x,y) coordinates of the vertex
\n" ); document.write( "For given equation: (y-3)^2=-8(x+2)
\n" ); document.write( "vertex: (-2,3)
\n" ); document.write( "4p=8
\n" ); document.write( "p=2
\n" ); document.write( "latus rectum=focal width=4p=8
\n" ); document.write( "focal point:(-4,3)
\n" ); document.write( "focal length=distance from vertex to focal point on axis of symmetry=p=2 \n" ); document.write( "
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