Question

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

Answer 1

x = (1/12) (y – 4)^2 – 5

Answer 2

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

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 (5,4)`

`vertex (2,4)`

substitute

`(h,k)=(2,4)`

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

so

Find the value of a

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

The equation of the horizontal parabola is equal to

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