Question

The line x = 2 is the axis of symmetry for a parabola. The focus of the parabola is located 3 units from the vertex.
Which could be the equation for the parabola?
(x – 2)2 = 12(y – k)
(x – h)2 = 12(y – 2)
(x – 2)2 = 3(y – k)
(x – h)2 = 3(y – 2)

Answer 1

A parabola with vertical axis has form (x − h)^2 = 4p(y − k). The axis x = 2 means h = 2, and the focus is p units from the vertex so |p| = 3, hence 4p = ±12. The choice that matches is

(x − 2)^2 = 12(y − k),

since 4p = 12 ⇒ p = 3.