Determine the focus of the parabola given by the equation x^2 = 8y.

₹0.0

Question: Determine the focus of the parabola given by the equation x^2 = 8y.

Options:

Correct Answer: (0, 4)

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).

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.

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).

Parabola Standard Form – Understanding the standard form of a parabola and how to identify its parameters.
Focus of a Parabola – Determining the focus based on the value of p derived from the standard form.