Find the length of the latus rectum of the parabola y^2 = 16x.

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Question: Find the length of the latus rectum of the parabola y^2 = 16x.

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Correct Answer: 8

Solution:

The length of the latus rectum of a parabola y^2 = 4px is given by 4p. Here, 4p = 16, so p = 4. Therefore, the length of the latus rectum is 4 * 4 = 16.

Find the length of the latus rectum of the parabola y^2 = 16x.

Practice Questions

Find the length of the latus rectum of the parabola y^2 = 16x.

Questions & Step-by-Step Solutions

Find the length of the latus rectum of the parabola y^2 = 16x.

Step 1: Identify the equation of the parabola. The given equation is y^2 = 16x.
Step 2: Compare the given equation with the standard form of a parabola, which is y^2 = 4px.
Step 3: From the standard form, identify that 4p = 16.
Step 4: Solve for p by dividing both sides of the equation by 4. So, p = 16 / 4 = 4.
Step 5: Use the formula for the length of the latus rectum, which is 4p.
Step 6: Substitute the value of p into the formula: Length of latus rectum = 4 * 4 = 16.

Parabola Properties – Understanding the standard form of a parabola and the relationship between its parameters, specifically how to derive the length of the latus rectum from the value of p.
Latus Rectum Calculation – Applying the formula for the length of the latus rectum (4p) to find the specific length based on the given equation of the parabola.

Find the length of the latus rectum of the parabola y^2 = 16x.

What’s inside this PDF?

Find the length of the latus rectum of the parabola y^2 = 16x.

Practice Questions

Questions & Step-by-Step Solutions

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