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Determine the focus of the parabola given by the equation x^2 = 8y.
Determine the focus of the parabola given by the equation x^2 = 8y.
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Practice Questions
1 question
Q1
Determine the focus of the parabola given by the equation x^2 = 8y.
(0, 2)
(0, 4)
(2, 0)
(4, 0)
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The standard form of the parabola is x^2 = 4py. Here, 4p = 8, so p = 2. The focus is at (0, p) = (0, 2).
Questions & Step-by-step Solutions
1 item
Q
Q: Determine the focus of the parabola given by the equation x^2 = 8y.
Solution:
The standard form of the parabola is x^2 = 4py. Here, 4p = 8, so p = 2. The focus is at (0, p) = (0, 2).
Steps: 6
Show Steps
Step 1: Identify the given equation of the parabola, which is x^2 = 8y.
Step 2: Recognize that the standard form of a parabola that opens upwards is x^2 = 4py.
Step 3: Compare the given equation x^2 = 8y with the standard form x^2 = 4py.
Step 4: From the comparison, identify that 4p = 8.
Step 5: Solve for p by dividing both sides of the equation 4p = 8 by 4, which gives p = 2.
Step 6: The focus of the parabola is located at the point (0, p). Since p = 2, the focus is at (0, 2).
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