Question

The curve described parametrically by \[ x = t^2 + 2t - 1, \quad y = 3t + 5 \] represents

• A. an ellipse
• B. a hyperbola
• C. a parabola
• D. a circle

Hint:

A parabola can be represented parametrically by quadratic equations in one variable and linear equations in another.

Answer 1

The Correct Option is C

Step 1: Recognizing the parametric form.
The given parametric equations describe a parabola because it is a quadratic equation in \( x \) and linear in \( y \).

Step 2: Conclusion.
Thus, the correct answer is option (C).

Final Answer: \[ \boxed{\text{(C) a parabola}} \]