The family of curves given by y^2 = 4ax represents which type of conic section?

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Question: The family of curves given by y^2 = 4ax represents which type of conic section?

Options:

Correct Answer: Parabola

Solution:

The equation y^2 = 4ax represents a parabola that opens to the right.

The family of curves given by y^2 = 4ax represents which type of conic section?

The family of curves given by y^2 = 4ax represents which type of conic section?

Step 1: Identify the equation given, which is y^2 = 4ax.
Step 2: Recognize that this equation is in the standard form of a parabola.
Step 3: Note that in the equation y^2 = 4px, the variable y is squared and the variable x is not, indicating a vertical orientation.
Step 4: Since the equation is y^2 = 4ax, it shows that the parabola opens to the right because 'a' is positive.
Step 5: Conclude that the family of curves represented by this equation is a parabola that opens to the right.

Conic Sections – The study of curves obtained by intersecting a cone with a plane, including parabolas, ellipses, and hyperbolas.
Parabola Characteristics – Understanding the standard form of a parabola and its orientation based on the equation.