Question

A parabola can be drawn given a focus of (6,-1) and a directrix of y = 9. What can be said about the parabola?​

Answer 1

Answer:

Since the focus is at (-6,-11) and the directrix is at y=9:

 

The vertex is halfway between the focus and the directrix, so the vertex is at (-6,-1).  (Draw this on graph paper if that doesn't make sense.)

 

The general form (conics form) of a parabola:  4p(y-k)=(x-h)^2 (vertex is (h,k) and "p" is the distance between the focus and vertex (or between vertex and directrix)).

 

(h,k) = (-6,-1)

 

p = 10 (distance between focus and vertex), so 4p = 40.

 

Therefore:

 

40(y+1)=(x+6)^2

 

Or if you need to rearrange to "vertex form":  y=(1/40)(x+6)^2 - 1

Step-by-step explanation: