Question

Parabolas A and B both have a focus at (2, 2). Parabola A has a directrix at x = -1 and parabola B has a directrix at x = 5. What is the distance between the vertices of the two parabolas?

A. 1.5
B. 3
C. 4
D. 5
E. 6

Answer 1

Parabola A: directrix is at x = -1 and focus is at (2,2) so the vertex is the midpoint between those. Vertex = (0.5, 2)

Parabola B: directrix is at x = 5 and focus is at (2,2) so the vertex is the midpoint between those. Vertex = (3.5, 2)

Distance between Vertex A and Vertex B is the distance between (0.5, 2) and (3.5, 2) = 3

Answer: B