Question

Derive the equation of the parabola with a focus at (−5, 5) and a directrix of y = -1.

f(x) = −(1/12) (x − 5)2 + 2

f(x) = (1/12) (x − 5)2 + 2

f(x) = -(1/12) (x + 5)2 + 2

f(x) = (1/12) (x + 5)2 + 2

Answer 1

@Hero

Answer 2

@phi

Answer 3

@thomaster

Answer 4

@austinL

Answer 5

@bookworm00981

Answer 6

As a first step, I would plot both the focus and the directrix (which is a line)
can you do that ?

Answer 7

The vertex of the parabola is exactly half way between the focus and the directrix
Can you plot it?

The parabola "curves around the focus".
Is it a smile or a frown? a smile will have a positive number multiplying the x term
a frown will have a minus sign in front of the (x-h)^2 term

Answer 8

expect a formula that looks like
\[ y = \frac{1}{4p} (x-h)^2 + k \]
where (h,k) is the coordinates of the vertex (1/2 between the focus and directrix)
p is 1/2 the distance between the focus and directrix
p is minus if the parabola is a frown.