Question

What is the directrix for the following parabola (x-1)^2 = 12(y+2)?

a) x = 1
b) x = -1
c) y = 2
d) y = -2

Answer 1

The directrix for the given parabola (x-1)^2 = 12(y+2) is x = -2.

Step-by-step explanation:

The equation of the given parabola is (x-1)^2 = 12(y+2). To find the directrix of the parabola, we can compare the given equation with the standard form of the parabola equation, which is (x-h)^2 = 4a(y-k). In this case, h = 1, k = -2, and a = 3. The directrix of the parabola is a vertical line given by the equation x = h - a, so the directrix for the given parabola is x = 1 - 3, which simplifies to x = -2.