a parabola has a vertex at the origin. the equation of the directrix of the parabola is y = 3. what are the…

Explanation:

Step1: Recall parabola property

For a parabola with vertex at origin $(0,0)$ and directrix $y = k$, if the directrix is a horizontal line $y=k$, the parabola opens either up - ward or downward. The distance from the vertex to the directrix is equal to the distance from the vertex to the focus.

Step2: Calculate distance

The directrix is $y = 3$, and the vertex is at $(0,0)$. The distance from the vertex $(0,0)$ to the directrix $y = 3$ is $|0 - 3|=3$. Since the parabola opens downward (because the directrix is above the vertex), the focus is 3 units below the vertex.

Step3: Find focus coordinates

The vertex is at $(0,0)$ and the focus is 3 units below it. So the coordinates of the focus are $(0,- 3)$.

Answer:

C. $(0,-3)$