Question

The distance from the green point on the parabola to the parabola's focus is 9 What is the distance from the green point to the directrix?

Answer 1

The correct answer is 9

Explanation:

Answer 2

Let the green point on the parabola be P.

Let the focus of the parabola be F.

Let M be the point on the directrix where the perpendicular from P intersects.

We know that for a conic,
`(FP)/(PM)=e` and for a parabola, e = 1.

So,
`(FP)/(PM) =1`

FP = PM

It is given that the distance between the green point and the focus is 9.

That is, FP = 9.

So, PM = 9.

Hence, the distance between the green point and the directrix = 9.