Question

What is the equation of the parabola with vertex (-5, 4) and focus (-2, 4)?

Answer 1

(X -5)^2 = 12(Y +4).

The standard form of a parabola (x - h)2 = 4p (y - k), where the focus is (h, k + p). I used the given information to plug in the numbers into the standard form equation.

Answer 2

`x=(1)/(12)(y-4)^(2)-5`

Explanation:

In this problem we have that

The vertex and the focus has the same y-coordinate, therefore, is a horizontal parabola

The equation of a horizontal parabola is of the form

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

where

(h,k) is the vertex

The coordinates of the focus are equal to
`(h+(1)/(4a) ,k)`

we have in this problem

`focus (-2,4)`

`vertex (-5,4)`

substitute

`(h,k)=(-5,4)`

`(-2,4)=(-5+(1)/(4a) ,4)`

so

Find the value of a

`-2=-5+(1)/(4a)\\ \\(1)/(4a)=3\\ \\a=(1)/(12)`

The equation of the horizontal parabola is equal to

`x=(1)/(12)(y-4)^(2)-5` ------> open to the right