Question

A parabola has a vertex at (0,0). The focus of the parabola is located at (4,0). What is the equation of the directrix?

Answer 1

the equation is y^2=16x and the directrix is x=-4

Answer 2

The equation of parabola is given by:

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

where,

(h, k) is the vertex.

Focus = (h+a, k)

As per the statement:

A parabola has a vertex at (0,0).

⇒
`y^2 = 4ax`

The focus of the parabola is located at (4,0).

⇒
`(h+a, k) = (4, 0)`

⇒
`(a, 0) = (4, 0)`

⇒a = 4

then, equation become:

`y^2 = 16x`

We have to find the equation of directrix

The equation of directrix is, x = h-a

then;

x = 0-4 = -4

⇒x = -4

Therefore, the equation of directrix is, x = -4