Question

The equation of a parabola is (y−3)2=20(x+1) .

What is the equation of the directrix of the parabola?

Answer 1

The equation of the directrix of the parabola is x=-6.

Explanation:

The given equation is

`(y-3)^2=20(x+1)` .... (1)

If a parabola is defined as

`(y-k)^2=4p(x-h)` .... (2)

Where, (h,k) is vertex and the directix of the parabola is x=h-p.

From (1) and (2), we get

`h=-1,k=3`

`4p=20`

`p=5`

The value of p is 5.

The equation of directix is

`x=h-p`

`x=-1-5`

`x=-6`

Therefore the equation of the directrix of the parabola is x=-6.

Answer 2

`x = - 6`

EXPLANATION

The given parabola has equation:

`{(y - 3)}^(2) = 20 {(x + 1)}^(2)`

This parabola opens in the direction of the positive x-axis.

This can be rewritten as:

`{(y - 3)}^(2) = 4(5) {(x + 1)}^(2)`

The vertex is (-1,3)

The directrix of this parabola is

`x = - 1 - 5`

`x = - 6`