Question

Derive the equation of the parabola with a focus at (2, 4) and a directrix of y = 8.

Answer 1

f(x) = −one eighth (x − 2)2 + 6

f(x) = one eighth (x − 2)2 + 6

f(x) = −one eighth (x + 2)2 + 8

f(x) = one eighth (x + 2)2 + 8

Answer 2

@_angeliquexoxo if you are given two points: the focus \((x_1, y_1)\) and the directrix \((x_2, y_2)\) you can insert them in to this formula:

\((x - x_1)^2 + (y - y_1)^2 = (x - x_2)^2 + (y - y_2)^2\)

In this case the focus is \((2, 4)\). The directrix is \((x, 8)\)

Answer 3

I have no idea what im supposed to do
@Hero

Answer 4

You insert the given points in to that formula like so:

\((x - 2)^2 + (y - 4)^2 = (x - x)^2 + (y - 8)^2\)

Afterwards simplify the equation since \((x - x)^2 = (0)^2 = 0\)
\((x - 2)^2 + (y - 4)^2 = (y - 8)^2\)

Next expand \((y - 4)^2\) and \((y - 8)^2\).

Finally solve for y

Answer 5

How do I solve for y.... I am so sorry I am a bit dumb with math :( @Hero

Answer 6

Have you attempted to expand \((y - 4)^2\) and \((y - 8)^2\) yet?

Answer 7

I would attempt to but I have no idea how to @Hero

Answer 8

ok... so looking at the information the directrix is above the focus... so the parabola is concave down... is that ok...?