
### Instruction: help me answer this question Find the equation of the parabola with equation x^2 = -9y., think step by step
### Assistant: On comparing the given equation with x^2 = -4ay, we get a = 9/4. The coordinates of the focus are (0,-a) = (0, -9/4). The given equation involves x^2, so the axis of the parabola is the y-axis. Therefore, the equation of directrix is y = a, which is y = 9/4. The length of latus rectum is 4a = 4(9/4) = 9. , The answer is x^2 = -9y.
