Question

Consider the parabola with a focus at the point (4,0) and directrix y = 3.

Answer 1

$\sqrt{x^{2} + y^{2}-8x +16}$ and mod(y-3)

Step-by-step explanation:

Step 1 :

Given the focus is at (4,0) and the directrix is y = 3. We have to find the 2 equations which relate the distance of the  given focus and the given directrix to any point (x, y) on the parabola

Step 2 :

The distance between a point P(x,y) given on the parabola and the focus (4,0)

is

$\sqrt{(x-4)^{2} + (y-0)^{2} } = \sqrt{x^{2}+16-8x + y^{2} } = \sqrt{x^{2} + y^{2}-8x +16}$

Step 3 :

The distance between the point P of (x,y) and the directrix line y = 3 is

mod (y-3)

So the 2 required equations are

$\sqrt{x^{2} + y^{2}-8x +16}$ and mod(y-3)