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Find the focus of the parabola defined by the equation x^2 = 12y.
Find the focus of the parabola defined by the equation x^2 = 12y.
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Practice Questions
1 question
Q1
Find the focus of the parabola defined by the equation x^2 = 12y.
(0, 3)
(0, -3)
(3, 0)
(-3, 0)
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The equation x^2 = 12y can be rewritten as (y - 0) = (1/3)(x - 0)^2, indicating the focus is at (0, 3).
Questions & Step-by-step Solutions
1 item
Q
Q: Find the focus of the parabola defined by the equation x^2 = 12y.
Solution:
The equation x^2 = 12y can be rewritten as (y - 0) = (1/3)(x - 0)^2, indicating the focus is at (0, 3).
Steps: 6
Show Steps
Step 1: Start with the given equation of the parabola: x^2 = 12y.
Step 2: Recognize that this is a standard form of a parabola that opens upwards, which can be written as y = (1/4p)x^2.
Step 3: Compare the given equation x^2 = 12y with the standard form y = (1/4p)x^2. Here, 12y = (1/4p)x^2.
Step 4: To find p, rewrite the equation as y = (1/12)x^2. This means 1/4p = 1/12.
Step 5: Solve for p by cross-multiplying: 4p = 12, so p = 3.
Step 6: The focus of a parabola that opens upwards is located at (0, p). Since p = 3, the focus is at (0, 3).
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