What is the general form of the family of curves represented by y^2 = 4ax?
Correct Answer: y^2 = 4ax
- Step 1: Identify the equation given, which is y^2 = 4ax.
- Step 2: Recognize that this equation is a standard form of a parabola.
- Step 3: Understand that in this equation, 'a' is a constant that affects the shape and position of the parabola.
- Step 4: Note that the parabola opens to the right because the 'y^2' term is positive and 'x' is on the right side of the equation.
- Step 5: Realize that different values of 'a' will create different parabolas, all of which open to the right.
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