Question

What is the standard form of the equation of the parabola with a directrix at x=-8 and a focus at (-7,3)?

Answer 1

`(y-3)^2=-4(15/2)(x-1/2)`

Explanation:

The directrix is x = 8 the focus S is (-7, 3), in the negative direction of x-axis, from the directrix..

Using the definition of the parabola as the locus of the point that is equdistant from the directrix and the focus, its equation is

`sqrt((x+7)^2+(y-3)^2)=8-x, > 0`,

as the parabola is on the focus-side of the directrix, in the negative x-direction.

Squaring, expanding and simplifying, the standard form is.

`(y-3)^2=-4(15/2)(x-1/2)`.

The axis of the parabola is y = 3, in the negative x-direction and the vertex V is (1/2, 3). The parameter for size, a = 15/2.,