Question

Write the equation of the parabola in vertex form

Answer 1

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

Explanation:

The general vertex form of parabola is,

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

where,

`(h.k)` is the vertex,

`y=h` is the axis of symmetry.

Given the coordinates of the vertex as
`(-2,0)` and focus as
`(-5,0)`

a is the 4 times the distance between the vertex and the focus.

The distance between the vertex and focus is -3. Negative is because we are calculating the distance to the left (-ve x direction) of the vertex.

Hence,
`a=4*(-3)=-12`

Putting the values in the general equation,

`(y-0)^2=-12(x-(-2))`

i.e
`y^2=-12(x+2)`