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Question 512206: Compute the focal length and the length of the latus rectum of the parabola y^2 + 8x - 6y + 25 = 0.
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Compute the focal length and the length of the latus rectum of the parabola y^2 + 8x - 6y + 25 = 0.
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y^2+8x-6y+25=0
complete the square
(y^2-6y+9)+8x+25-9=0
(y-3)^2+8x+16=0
(y-3)^2+8(x+2)=0
(y-3)^2=-8(x+2)
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
For given equation: (y-3)^2=-8(x+2)
vertex: (-2,3)
4p=8
p=2
latus rectum=focal width=4p=8
focal point:(-4,3)
focal length=distance from vertex to focal point on axis of symmetry=p=2
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