Parametric and Cartesian forms Quiz

1. For $x=t-1$, $y=t^2$, what is the Cartesian equation?

• A. $y=(x-1)^2$
• B. $y=x^2-1$
• C. $y=(x+1)^2$
• D. $y=x^2+1$

2. The curve $x=3\cos\theta$, $y=3\sin\theta$ is:

• A. a circle of radius $3$
• B. a circle of radius $9$
• C. an ellipse
• D. a straight line

3. For $x=5t$, $y=1-t^2$, find $y$ in terms of $x$.

• A. $y=1-5x^2$
• B. $y=1+\dfrac{x^2}{25}$
• C. $y=1-\dfrac{x^2}{5}$
• D. $y=1-\dfrac{x^2}{25}$

4. At what value of $t$ does $x=2t-6$, $y=t^2$ cross the $y$-axis?

• A. $t=6$
• B. $t=3$
• C. $t=-3$
• D. $t=0$

5. A curve has $y=x^3$. Which is a valid parametric form?

• A. $x=t^3$, $y=t$
• B. $x=t$, $y=t^3$
• C. $x=t^3$, $y=t^3$
• D. $x=t$, $y=3t$