If the equation of a parabola is given by y^2 = 12x, what is the value of 'p'?

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Question: If the equation of a parabola is given by y^2 = 12x, what is the value of \'p\'?

Options:

Correct Answer: 6

Solution:

In the equation y^2 = 4px, p = 3, hence the value of \'p\' is 3.

If the equation of a parabola is given by y^2 = 12x, what is the value of 'p'?

If the equation of a parabola is given by y^2 = 12x, what is the value of 'p'?

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 = 12x with the standard form y^2 = 4px.
Step 3: Notice that in the standard form, 4p is equal to the coefficient of x in the given equation.
Step 4: In the equation y^2 = 12x, the coefficient of x is 12, so we set 4p = 12.
Step 5: To find p, divide both sides of the equation 4p = 12 by 4.
Step 6: This gives p = 12 / 4, which simplifies to p = 3.

Parabola Standard Form – Understanding the standard form of a parabola, specifically y^2 = 4px, and how to identify the value of 'p' from it.