What is the latus rectum of the parabola given by the equation y^2 = 12x?

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Question: What is the latus rectum of the parabola given by the equation y^2 = 12x?

Options:

Correct Answer: 6

Solution:

The latus rectum of a parabola y^2 = 4px is given by 4p. Here, 4p = 12, so p = 3, and the latus rectum is 4p = 12.

What is the latus rectum of the parabola given by the equation y^2 = 12x?

What is the latus rectum of the parabola given by the equation y^2 = 12x?

Step 1: Identify the standard form of the parabola. The given equation is y^2 = 12x, which is in the form y^2 = 4px.
Step 2: Compare the given equation with the standard form. Here, 4p = 12.
Step 3: Solve for p by dividing both sides of the equation by 4. So, p = 12 / 4 = 3.
Step 4: Use the value of p to find the latus rectum. The latus rectum is given by the formula 4p.
Step 5: Calculate the latus rectum using p. So, latus rectum = 4 * 3 = 12.

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