Question

What is the equation of a parabola satisfying the given information? Focus​ (8​, 4​), directrix x= -9

Answer 1

`(y-4)^2=34(x+0.5)`

Explanation:

Given -
Focus `(8, 4)`
Ditectrix `x=-9`

Calculate vertex

`(-9+8)/2, (4+4)/2=(-0.5, 4)`

Calculate `a`

`a=sqrt((-0.5 -8)^2)=sqrt72.25=8.5`

Based on the information, the parabola opens right.

Given vertex and `a` the equation is -

`y^2=4ax`

Since the origin is `(-0.5,4)`

The equation is

`(y-k)^2=4 xx a xx (x-h)`

Where -

`h=-0.5`
`k=4`
`a=8.5`

Substitute these values in the equation

`(y-4)^2=4 xx 8.5 xx(x+0.5)`

`(y-4)^2=34(x+0.5)`