Question

Find an equation of a parabola satisfying the given information. Focus (8,0), directrix x= - 8 An equation for a parabola satisfying these conditions is (Type an equation. Simplify your answer.) .

Answer 1

Answer:- $y^{2}=32x$

Explanation:-

It is given that the directrix of the parabola is x =- 8 and focus is (8, 0).

Since focus lies on x-axis.

Hence equation is either $y^{2}=4ax$ or$y^{2}=-4ax$

Now, focus has positive x coordinates

so, we have to use the equation $y^{2}=4ax$

Coordinates of focus = (a,0)

(8,0)=(a,0)

Hence a=8

Required equation is $y^{2}=4ax$

$y^{2}=32x$

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