Focus-directrix properties and eccentricity Quiz

1. The ellipse $\frac{x^2}{36}+\frac{y^2}{20}=1$ has eccentricity

• A. $\frac49$
• B. $\frac59$
• C. $\frac29$
• D. $\frac23$

2. A hyperbola has $a=4$ and $e=\frac32$. Its directrices are

• A. $x=\pm\frac83$
• B. $x=\pm6$
• C. $x=\pm\frac{16}{3}$
• D. $x=\pm4$

3. Which eccentricity gives a hyperbola?

• A. $e=\frac12$
• B. $e=\frac34$
• C. $e=2$
• D. $e=0.9$

4. The foci of $\frac{x^2}{25}+\frac{y^2}{9}=1$ are

• A. $(\pm5,0)$
• B. $(\pm4,0)$
• C. $(\pm3,0)$
• D. $(0,\pm4)$

5. Which statement is the focus-directrix property?

• A. $PS=e\times PM$
• B. $PS+PM=e$
• C. $PS=\frac{PM}{e}$
• D. $PS\times PM=e$