What is the value of p for the parabola defined by the equation x^2 = 16y?

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Question: What is the value of p for the parabola defined by the equation x^2 = 16y?

Options:

Correct Answer: 4

Solution:

In the equation x^2 = 4py, we have 4p = 16, thus p = 4.

What is the value of p for the parabola defined by the equation x^2 = 16y?

What is the value of p for the parabola defined by the equation x^2 = 16y?

Step 1: Start with the given equation of the parabola, which is x^2 = 16y.
Step 2: Compare this equation with the standard form of a parabola, which is x^2 = 4py.
Step 3: In the standard form, 4p is the coefficient of y. Here, we see that 4p = 16.
Step 4: To find the value of p, divide both sides of the equation 4p = 16 by 4.
Step 5: This gives us p = 16 / 4.
Step 6: Simplifying this, we find p = 4.

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