The general form of the family of curves y^2 = 4ax represents:

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Question: The general form of the family of curves y^2 = 4ax represents:

Options:

Correct Answer: Parabolas

Solution:

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

The general form of the family of curves y^2 = 4ax represents:

The general form of the family of curves y^2 = 4ax represents:

Step 1: Identify the equation given, which is y^2 = 4ax.
Step 2: Recognize that this is a standard form of a parabola equation.
Step 3: Understand that in this equation, 'a' is a constant that determines the width and position of the parabola.
Step 4: Note that the 'y^2' term indicates that the parabola opens either to the right or left, depending on the sign of 'a'.
Step 5: Since '4a' is positive when 'a' is positive, the parabola opens to the right.

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