document.write( "Question 949635: find the coordinates of the vertex, focus, and endpoints of the latus rectum. also find the equation of the directrix of 4x^2-16x-15y+1=0. \n" ); document.write( "
Algebra.Com's Answer #579780 by lwsshak3(11628)\"\" \"About 
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find the coordinates of the vertex, focus, and endpoints of the latus rectum. also find the equation of the directrix of 4x^2-16x-15y+1=0.
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\n" ); document.write( "basic form of equation for parabola that opens upward: (x-h)^2=4p(y-k), (h,k)=coordinates of the vertex.
\n" ); document.write( "complete the square:
\n" ); document.write( "4(x^2-4x+4)-16-15y+1=0
\n" ); document.write( "4(x-2)^2=15y+15
\n" ); document.write( "4(x-2)^2=15(y+1)
\n" ); document.write( "(x-2)^2=(15/4)(y+1)
\n" ); document.write( "vertex: (2,-1)
\n" ); document.write( "axis of symmetry: x=2
\n" ); document.write( "4p=15/4
\n" ); document.write( "p=15/16
\n" ); document.write( "focus: (2,-1/16) (p-distance above vertex on the axis of symmetry)
\n" ); document.write( "directrix :y=31/16 (p-distance below vertex on the axis of symmetry)
\n" ); document.write( "endpoints of latus rectum:
\n" ); document.write( "(x-2)^2=(15/4)(y+1)
\n" ); document.write( "y=-1/16
\n" ); document.write( "(x-2)^2=(15/4)(-1/16+1)
\n" ); document.write( "(x-2)^2=(15/4)(15/16)
\n" ); document.write( "(x-2)^2=(15^2/64)
\n" ); document.write( "take sqrt of both sides
\n" ); document.write( "x-2=±15/8
\n" ); document.write( "x=2±15/8=16/8±15/8=1/8, 31/8
\n" ); document.write( "endpoints of latus rectum: (1/8,-1/16) and (31/8, -1/16)
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