Q. What is the length of the latus rectum of the parabola y^2 = 12x?
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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.
Correct Answer: B — 6
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Q. What is the value of p for the parabola defined by the equation x^2 = 16y?
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Solution
In the equation x^2 = 4py, we have 4p = 16, thus p = 4.
Correct Answer: B — 4
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Q. What is the value of p for the parabola given by the equation x^2 = 20y?
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Solution
In the equation x^2 = 4py, we have 4p = 20, thus p = 20/4 = 5.
Correct Answer: A — 5
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Q. What is the vertex of the parabola defined by the equation y = -2(x - 1)^2 + 4?
A.
(1, 4)
B.
(1, -4)
C.
(4, 1)
D.
(-1, 4)
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Solution
The vertex form of a parabola is y = a(x - h)^2 + k. Here, h = 1 and k = 4, so the vertex is (1, 4).
Correct Answer: A — (1, 4)
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Q. What is the vertex of the parabola given by the equation y = -2(x - 1)^2 + 4?
A.
(1, 4)
B.
(1, -4)
C.
(4, 1)
D.
(-1, 4)
Show solution
Solution
The vertex form of a parabola is y = a(x - h)^2 + k. Here, h = 1 and k = 4, so the vertex is (1, 4).
Correct Answer: A — (1, 4)
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Q. What is the vertex of the parabola represented by the equation y = -2(x - 1)^2 + 4?
A.
(1, 4)
B.
(1, -4)
C.
(-1, 4)
D.
(-1, -4)
Show solution
Solution
The vertex form of a parabola is y = a(x - h)^2 + k. Here, h = 1 and k = 4, so the vertex is (1, 4).
Correct Answer: A — (1, 4)
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