Question

a parabola has a vertex at the origin. the equation of the directrix of the parabola is y = 3. what are the coordinates of its focus? (0,3) (3,0) (0, - 3) (-3,0)

Explanation:

Step1: Recall parabola property

The vertex of the parabola is at the origin \((0,0)\) and the directrix is \(y = 3\). For a parabola with vertex at the origin, the focus and directrix are equidistant from the vertex.

Step2: Determine focus - directrix relationship

Since the directrix \(y = 3\) is a horizontal line above the vertex \((0,0)\), the parabola opens down - ward. The distance between the vertex and the directrix is \(d=3\). The focus is at the same distance from the vertex as the directrix, but in the opposite direction. So the \(y\) - coordinate of the focus is \(y=- 3\) and the \(x\) - coordinate is \(x = 0\).

Answer:

C. \((0,-3)\)