Identify the family of curves represented by the equation y^2 = 4ax.
Correct Answer: Parabolas opening to the right
- Step 1: Start with the equation y^2 = 4ax.
- Step 2: Recognize that this is a quadratic equation in terms of y.
- Step 3: Identify the standard form of a parabola, which is y^2 = 4px, where p is a constant.
- Step 4: In our equation, 4a is equivalent to 4p, meaning a = p.
- Step 5: Understand that 'a' can take any positive value, which means the shape of the parabola changes.
- Step 6: Conclude that the equation represents a family of parabolas that all open to the right.
- Parabolas – The equation y^2 = 4ax describes parabolas that open to the right, where 'a' determines the width and position of the parabola.
