Question

The focus of a parabola is (3, -2), and the directrix is x = -5. What are the vertex and the axis of symmetry of the parabola?

a) Vertex: (3, -2), Axis of symmetry: x = -1
b) Vertex: (3, -2), Axis of symmetry: x = 1
c) Vertex: (3, -2), Axis of symmetry: x = 3
d) Vertex: (3, -2), Axis of symmetry: x = -3

Answer 1

The vertex of the parabola is (-1, -2) and the axis of symmetry is x = -1.

Step-by-step explanation:

The vertex of a parabola can be found by finding the midpoint between the focus and the directrix. In this case, the focus is (3, -2) and the directrix is x = -5. The x-coordinate of the vertex is the average of the x-coordinates of the focus and the directrix, which is (3 + (-5))/2 = -1. The y-coordinate of the vertex is the same as the y-coordinate of the focus, which is -2. Therefore, the vertex of the parabola is (-1, -2).

The axis of symmetry is a vertical line that passes through the vertex. In this case, the equation of the axis of symmetry is x = -1.