Question

Find the focus and directrix of the parabola represented by the equation y = -120x² + 32:

A) Focus: (-60, 16), Directrix: x = -1
B) Focus: (0, 32), Directrix: y = -1
C) Focus: (0, 16), Directrix: y = -1
D) Focus: (60, 16), Directrix: x = 1

Answer 1

The focus of the parabola is at (0, -30) and the directrix is x = 30.

Step-by-step explanation:

The equation of the parabola is given by y = -120x² + 32. To find the focus and directrix, we need to express the equation in the form y = 4px.

Comparing the given equation to the standard form, we have 4p = -120, so p = -30.

The focus is located at (0, p), so the focus is (0, -30).

The directrix is a vertical line given by x = -p, so the directrix is x = 30.