Question

Find the equation with vertex(-2,5) and focus(1,5)​

Answer 1

`(y-5)^2=12(x+2)`

Explanation:

Since the focus point is directly right of the vertex, the axis of symmetry will be horizontal, which means that we use the equation
`(y-k)^2=4p(x-h)` where
`(h,k)` is the vertex and
`(h+p,k)` is the focus point.

Since we know our vertex to be
`(h,k)\rightarrow(-2,5)` and our focus point to be
`(h+p,k)\rightarrow(1,5)`, the distance from the vertex to the focus point is
`p=3`.

Hence, the equation is:

`(y-5)^2=4(3)(x-(-2))\\\\(y-5)^2=12(x+2)`