What is the equation in standard form of the parabola with a focus at (14,15) and a directrix of y= -7?

Question

Ethan Adkins · Accepted Answer

The equation of parabola is #y=1/88(x-14)^2+15# The standard equation of parabola is #y=a(x-h)^2+k# where #(h,k)# is the vertex. So the equation of parabola is #y=a(x-14)^2+15# The distance of the vertex from the directrix #(y=-7)# is #15+7=22 :. a = 1/(4d)=1/(4*22)=1/88#. Hence equation of parabola is #y=1/88(x-14)^2+15# graph{1/88(x-14)^2+15 [-160, 160, -80, 80]}[Ans]

Savannah Anderson · Answer

undefined The equation in standard form of the parabola with a focus at (14,15) and a directrix of y= -7 is:

(x - h)^2 = 4p(y - k)

where (h, k) is the vertex of the parabola and p is the distance between the vertex and the focus (or the vertex and the directrix).

Given the focus (14,15) and the directrix y= -7:
1. The vertex is halfway between the focus and the directrix, so the vertex is (14, 4).
2. The distance between the focus and the vertex is the same as the distance between the directrix and the vertex, which is 15 - (-7) = 22.
3. Since the parabola opens upward, p = 22.

Plugging in the values:
(x - 14)^2 = 4 * 22(y - 4)