What is the focus of the parabola defined by the equation y^2 = 20x?

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Question: What is the focus of the parabola defined by the equation y^2 = 20x?

Options:

Correct Answer: (5, 0)

Solution:

In the equation y^2 = 4px, we have 4p = 20, thus p = 5. The focus is at (5, 0).

What is the focus of the parabola defined by the equation y^2 = 20x?

What is the focus of the parabola defined by the equation y^2 = 20x?

Step 1: Identify the given equation, which is y^2 = 20x.
Step 2: Compare the given equation with the standard form of a parabola, which is y^2 = 4px.
Step 3: In the standard form, 4p represents the coefficient of x. Here, we see that 4p = 20.
Step 4: To find p, divide both sides of the equation 4p = 20 by 4. This gives p = 20 / 4.
Step 5: Calculate p, which equals 5.
Step 6: The focus of the parabola is located at the point (p, 0). Since we found p = 5, the focus is at (5, 0).

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