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

₹0.0

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

Options:

Correct Answer: (5, 0)

Solution:

For the parabola y^2 = 4px, here 4p = 20, so p = 5. The focus is at (5, 0).

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

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

Step 1: Identify the given equation of the parabola, which is y^2 = 20x.
Step 2: Recognize that the standard form of a parabola that opens to the right is y^2 = 4px.
Step 3: Compare the given equation y^2 = 20x with the standard form y^2 = 4px.
Step 4: From the comparison, identify that 4p = 20.
Step 5: Solve for p by dividing both sides of the equation by 4: p = 20 / 4.
Step 6: Calculate p, which gives p = 5.
Step 7: The focus of the parabola is located at the point (p, 0).
Step 8: Substitute the value of p into the focus coordinates: (5, 0).

No concepts available.