What is the length of the latus rectum of the parabola y^2 = 12x?
Practice Questions
1 question
Q1
What is the length of the latus rectum of the parabola y^2 = 12x?
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12
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The length of the latus rectum of a parabola given by the equation y^2 = 4px is 4p. Here, 4p = 12, so p = 3. Therefore, the length of the latus rectum is 4p = 12.
Questions & Step-by-step Solutions
1 item
Q
Q: What is the length of the latus rectum of the parabola y^2 = 12x?
Solution: The length of the latus rectum of a parabola given by the equation y^2 = 4px is 4p. Here, 4p = 12, so p = 3. Therefore, the length of the latus rectum is 4p = 12.
Steps: 7
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.
