For the parabola defined by the equation x^2 = 16y, what is the length of the la

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Question: For the parabola defined by the equation x^2 = 16y, what is the length of the latus rectum?

Options:

Correct Answer: 8

Solution:

The length of the latus rectum for the parabola x^2 = 4py is 4p. Here, p = 4, so the length is 8.

For the parabola defined by the equation x^2 = 16y, what is the length of the latus rectum?

For the parabola defined by the equation x^2 = 16y, what is the length of the latus rectum?

Step 1: Identify the standard form of the parabola. The equation x^2 = 16y is in the form x^2 = 4py.
Step 2: Compare the given equation x^2 = 16y with the standard form x^2 = 4py. Here, 4p = 16.
Step 3: Solve for p by dividing both sides of the equation 4p = 16 by 4. This gives p = 4.
Step 4: Use the formula for the length of the latus rectum, which is 4p. Since we found p = 4, we calculate 4p = 4 * 4.
Step 5: Calculate 4 * 4, which equals 16. Therefore, the length of the latus rectum is 16.

Parabola Properties – Understanding the standard form of a parabola and the definition of the latus rectum.
Parameter p – Identifying the value of p in the equation of the parabola and its relation to the latus rectum.