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

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

Options:

Correct Answer: x = -5

Solution:

For the equation y^2 = 4px, p = 5. The directrix is given by x = -p, which is x = -5.

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

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

Step 1: Identify the standard form of a parabola that opens to the right, which is y^2 = 4px.
Step 2: Compare the given equation y^2 = 20x with the standard form y^2 = 4px.
Step 3: From the equation y^2 = 20x, we can see that 4p = 20.
Step 4: Solve for p by dividing both sides of the equation by 4: p = 20 / 4 = 5.
Step 5: The directrix of a parabola is given by the equation x = -p.
Step 6: Substitute the value of p into the directrix equation: x = -5.

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