Question

Right an equation of a problem given the vertex and the focus

Answer 1

Given:

A parabola has a vertex (1, -1) and direcrix (x = -5)

The general equation of the parabola will be as follows:

`(y-k)^2=\pm4a(x-h)`

where the vertex = (h, k)

So, h = 1, k = -1

We will choose the positive sign because the directrix is on the left of the vertex.

the value of (a) is the distance between the vertex and the directrix

`a=1-(-5)=6`

So, the equation of the parabola will be as follows:

`\begin{gathered} (y+1)^2=4*6(x-1) \\ \\ (y+1)^2=24(x-1) \end{gathered}`