What is the equation in standard form of the parabola with a focus at (-10,-9) and a directrix of y= -4?

1 Answer
Binayaka C.
Feb 10, 2017

The equation of parabola is y = -1/10(x+10)^2 -6.5

Explanation:

The focus is at (-10 , -9) Directrix: y =-4 . Vertex is at mid point between focus and directrix. So vertex is at (-10, (-9-4)/2) or (-10, -6.5) and the parabola opens downwards (a = -ive )

The equation of parabola is y= a(x-h)^2 =k or y = a(x -(-10))^2+ (-6.5) or y= a(x+10)^2 -6.5 where (h,k) is vertex.

The distance between vertex and directrix , d=6.5-4.0=2.5 = 1/(4|a|) :. a = -1/(4*2.5) = -1/10

Hence the equation of parabola is y = -1/10(x+10)^2 -6.5 graph{ -1/10(x+10)^2 - 6.5 [-40, 40, -20, 20]} [Ans]

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