What is the length of the latus rectum of the parabola y^2 = 12x?

What is the length of the latus rectum of the parabola y^2 = 12x?

Step 1: Identify the equation of the parabola. The given equation is y^2 = 12x.
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 = 12.
Step 4: Solve for p by dividing both sides of the equation by 4. So, p = 12 / 4 = 3.
Step 5: Use the value of p to find the length of the latus rectum. The formula for the length of the latus rectum is 4p.
Step 6: Substitute the value of p into the formula: 4p = 4 * 3 = 12.
Step 7: Conclude that the length of the latus rectum of the parabola y^2 = 12x is 12.

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