Question

C

X
A parabola has a focus at ( 1.5, 0) and a directrix of x= -1.5. Which of the following equations represent the parabola?

Answer 1

Explanation:

Since the focus lies on the x axis, and the diretcrtirx is a vertical line, we have a sideways parabola so we have the equation

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

where h,k is the vertex and

p is the distance from the vertex to the focus or the distance fromcthe vertex to the directrix.

Since the focus is 1.5, and the directrix is -1.5 the vertex is (0,0) so we have

`y {}^(2) = 4px`

We know p is 1.5 so we have

`{y}^(2) = 6x`

`(1)/(6 ) {y}^(2) = x`