The equation of a parabola is given by x^2 = 16y. What is the length of the latu

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Question: The equation of a parabola is given by 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 given by 4p. Here, 4p = 16, so p = 4. Thus, the length of the latus rectum is 4p = 16.

The equation of a parabola is given by x^2 = 16y. What is the length of the latus rectum?

The equation of a parabola is given by x^2 = 16y. What is the length of the latus rectum?

Step 1: Identify the given equation of the parabola, which is x^2 = 16y.
Step 2: Recognize that the standard form of a parabola that opens upwards is x^2 = 4py.
Step 3: Compare the given equation x^2 = 16y with the standard form x^2 = 4py to find the value of 4p.
Step 4: From the equation, we see that 4p = 16.
Step 5: To find p, divide both sides of the equation 4p = 16 by 4. This gives p = 4.
Step 6: The length of the latus rectum for a parabola is given by the formula 4p.
Step 7: Substitute the value of p into the formula: 4p = 4 * 4 = 16.
Step 8: Conclude that the length of the latus rectum is 16.

Parabola Properties – Understanding the standard form of a parabola and the relationship between its parameters, specifically the length of the latus rectum.
Latus Rectum Calculation – Applying the formula for the length of the latus rectum, which is 4p, where p is the distance from the vertex to the focus.