Question

Choose the correct equation for the parabola based on the given information. Given: Focus:(2,8) Directrix: y = 4 a. 2(y-2)= (x- 6)^2 b. 8(x -2) = (y -6)^2 c. 8(y - 6)= (x-2)^2 d. 2(x-2)= (y-8)^2

Answer 1

Answer:  c. 8(y-6) = (x-2)^2

Explanation:

The directrix is horizontal, so the axis of symmetry is vertical. We'll have an x^2 term. The vertical distance from y = 4 to y = 8 is 4 units. Cut this in half to get 2, which is the focal distance p = 2.

The point (2,4) is directly below (2,8), and the point is on the directrix. The midpoint between (2,4) and (2,8) is (2,6). This is the vertex.

(h,k) = (2,6)

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

4*2(y-6) = (x-2)^2

8(y-6) = (x-2)^2