Find the focus of the parabola given by the equation y^2 = 12x.

₹0.0

Question: Find the focus of the parabola given by the equation y^2 = 12x.

Options:

Correct Answer: (0, 6)

Solution:

The standard form of a parabola is y^2 = 4px. Here, 4p = 12, so p = 3. The focus is at (p, 0) = (3, 0).

Find the focus of the parabola given by the equation y^2 = 12x.

Find the focus of the parabola given by the equation y^2 = 12x.

Step 1: Identify the given equation of the parabola, which is y^2 = 12x.
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 = 12x with the standard form y^2 = 4px to find the value of 4p.
Step 4: From the equation, we see that 4p = 12.
Step 5: To find p, divide both sides of the equation by 4: p = 12 / 4.
Step 6: Calculate p, which gives p = 3.
Step 7: The focus of the parabola is located at the point (p, 0).
Step 8: Substitute the value of p into the focus point: (3, 0).

Parabola Standard Form – Understanding the standard form of a parabola (y^2 = 4px) and how to identify parameters.
Focus of a Parabola – Knowing that the focus of a parabola in the form y^2 = 4px is located at (p, 0).