Consider the parabola with a focus at the point (4,0) and directrix y = 3.
Which two equations can be used to correctly relate the distances from the
focus and the directrix to any point (x, y) on the parabola?

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

[tex]\sqrt{(x-4)^{2} + (y-0)^{2} } = \sqrt{x^{2}+16-8x + y^{2} } = \sqrt{x^{2} + y^{2}-8x +16}[/tex]

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

[tex]\sqrt{x^{2} + y^{2}-8x +16}[/tex] and mod(y-3)

waternoah waternoah · Answer 2 · 2025-03-27T18:38:57-04:00

waternoah waternoah

Today at 6:38 PM

Answer:

View attached image

Step-by-step explanation:

First formula is directrix-y

Second formula is the distance formula. Just plug in the (x,y) into it.

Answer Link

Consider the parabola with a focus at the point (4,0) and directrix y = 3. Which two equations can be used to correctly relate the distances from the focus and the directrix to any point (x, y) on the parabola?

Answer :

Other Questions

Consider the parabola with a focus at the point (4,0) and directrix y = 3.
Which two equations can be used to correctly relate the distances from the
focus and the directrix to any point (x, y) on the parabola?