What is the length of the latus rectum of the parabola y^2 = 8x?

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Question: What is the length of the latus rectum of the parabola y^2 = 8x?

Options:

Correct Answer: 4

Solution:

The length of the latus rectum of the parabola y^2 = 8x is 4.

What is the length of the latus rectum of the parabola y^2 = 8x?

What is the length of the latus rectum of the parabola y^2 = 8x?

Step 1: Identify the standard form of the parabola. The equation y^2 = 8x is in the standard form y^2 = 4px.
Step 2: Compare the given equation with the standard form. Here, 4p = 8.
Step 3: Solve for p by dividing both sides of the equation by 4. So, p = 8 / 4 = 2.
Step 4: The length of the latus rectum of a parabola is given by the formula 4p.
Step 5: Substitute the value of p into the formula. So, the length of the latus rectum = 4 * 2 = 8.
Step 6: Conclude that the length of the latus rectum of the parabola y^2 = 8x is 8.

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