A parabola has the focus at (4, 6) and the directrix y = –6. Which equation represents this parabola? (x – 4)2 = 24y
(x – 4)2 = StartFraction 1 Over 24 EndFractiony
(x – 4)2 = –24y
(x – 4)2 = Negative StartFraction 1 Over 24 EndFractiony

Step-by-step explanation:

If you graph both the focus and the directrix you will see that the directrix is below the focus...12 units below to be exact. The focus is on the vertical line x = 4, so the vertex also has an x coordinate (which is actually h since h and k represent the vertex) of 4. The vertex is exactly halfway between the focus and the directrix, so that means that the vertex is at (4, 0). h = 4, k = 0. The standard form for this parabola (we know it opens upwards since the parabola ALWAYS wraps itself around the focus and is directed away from the directrix) is:

p is the number of units between the focus and the vertex, or the vertex and the directrix (which is the same number of units since the vertex is smack dab in the middle of them!). That means that p = 6. Filling in 6 for p, 4 for h, and 0 for k we have:

and simplify to

which is the first choice you're given.

the solution is 12x-6y