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Determine the length of the latus rectum of the parabola y^2 = 16x.
Determine the length of the latus rectum of the parabola y^2 = 16x.
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Practice Questions
1 question
Q1
Determine the length of the latus rectum of the parabola y^2 = 16x.
4
8
16
32
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The length of the latus rectum for the parabola y^2 = 4px is given by 4p. Here, p = 4, so the length is 16.
Questions & Step-by-step Solutions
1 item
Q
Q: Determine the length of the latus rectum of the parabola y^2 = 16x.
Solution:
The length of the latus rectum for the parabola y^2 = 4px is given by 4p. Here, p = 4, so the length is 16.
Steps: 5
Show Steps
Step 1: Identify the standard form of the parabola. The given equation is y^2 = 16x.
Step 2: Compare the given equation with the standard form y^2 = 4px. Here, 4p = 16.
Step 3: Solve for p by dividing both sides of the equation 4p = 16 by 4. This gives p = 4.
Step 4: Use the formula for the length of the latus rectum, which is 4p.
Step 5: Substitute p = 4 into the formula: Length = 4 * 4 = 16.
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