Question

What is the equation of the quadratic graph with a focus of (8, −8) and a directrix of y = −6? and can someone show me how to solve problems like this?

Answer 1

i have two others like this

What is the equation of the quadratic graph with a focus of (4, −3) and a directrix of y = −6?

and

What is the equation of the quadratic graph with a focus of (1, 1) and a directrix of y = −1?

but if someone could just tell me how to solve these that'd be cool too

Answer 2

ok... there are several ways to do this

I start by graphing things so I know what I'm looking at



so looking at things... the directrix is above the focus so the parabola is concave down.

so then I know the general form of the curve is

\[(x -h)^2 = -4a(y - k)\]

where (h, k) is the vertex and a is the focal length.