What is the equation of the directrix of the parabola x^2 = 12y?

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Question: What is the equation of the directrix of the parabola x^2 = 12y?

Options:

Correct Answer: y = -3

Solution:

The directrix of the parabola x^2 = 4py is given by y = -p. Here, p = 3, so the directrix is y = -3.

What is the equation of the directrix of the parabola x^2 = 12y?

What is the equation of the directrix of the parabola x^2 = 12y?

Step 1: Identify the standard form of the parabola. The equation x^2 = 12y can be rewritten in the form x^2 = 4py.
Step 2: Compare the equation x^2 = 12y with x^2 = 4py. Here, we see that 4p = 12.
Step 3: Solve for p by dividing both sides of the equation 4p = 12 by 4. This gives p = 12 / 4 = 3.
Step 4: The directrix of a parabola in this form is given by the equation y = -p.
Step 5: Substitute the value of p into the directrix equation. Since p = 3, we have y = -3.

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