The rectangular hyperbola Quiz

1. Find the Cartesian equation of the curve $x=4t$, $y=\frac4t$.

• A. $xy=4$
• B. $xy=16$
• C. $x+y=4$
• D. $y=\frac{4}{x^2}$

2. A rectangular hyperbola has equation $xy=9$, with $x=3t$ and $y=\frac3t$. Find the point with parameter $t=-2$.

• A. $\left(6,\frac32\right)$
• B. $\left(-6,\frac32\right)$
• C. $\left(-\frac32,-6\right)$
• D. $\left(-6,-\frac32\right)$

3. The point $(2,18)$ lies on $xy=c^2$ with $c>0$. Find $c$.

• A. $6$
• B. $36$
• C. $20$
• D. $9$

4. On $x=3t$, $y=\frac3t$ the point has $x=12$. Find its $y$-coordinate.

• A. $4$
• B. $36$
• C. $\frac34$
• D. $\frac14$

5. On $xy=16$ (parametric form $x=4t$, $y=\frac4t$), which point has parameter $t=\frac12$?

• A. $(8,2)$
• B. $(2,8)$
• C. $\left(4,\frac12\right)$
• D. $\left(\frac12,8\right)$