Ellipse and hyperbola Quiz

1. What is the eccentricity of $\frac{x^2}{36}+\frac{y^2}{20}=1$?

• A. $\frac49$
• B. $\frac23$
• C. $\frac59$
• D. $\frac32$

2. What are the foci of $\frac{x^2}{16}-\frac{y^2}{9}=1$?

• A. $(\pm7,0)$
• B. $(\pm\sqrt7,0)$
• C. $(\pm4,0)$
• D. $(\pm5,0)$

3. For which condition is $y=mx+c$ a tangent to $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$?

• A. $c^2=a^2m^2-b^2$
• B. $c^2=a^2m^2+b^2$
• C. $c^2=b^2m^2-a^2$
• D. $c=\frac am$

4. What is the point with $t=\frac\pi6$ on $\frac{x^2}{9}+\frac{y^2}{4}=1$, using $x=3\cos t$, $y=2\sin t$?

• A. $\left(\frac32,\sqrt3\right)$
• B. $\left(\frac{3\sqrt3}{2},\sqrt3\right)$
• C. $\left(\frac{3\sqrt3}{2},1\right)$
• D. $\left(\frac32,1\right)$

5. What is $\frac{dy}{dx}$ at $(x,y)$ on $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$?

• A. $\frac{b^2x}{a^2y}$
• B. $-\frac{b^2x}{a^2y}$
• C. $-\frac{a^2x}{b^2y}$
• D. $-\frac xy$