Question

The arrangement of the following conics in the ascending order of their eccentricities is
A) $r(4+\cos \theta )=8$
B) $\frac{1}{r}=\frac{3}{5}-\frac{3\cos \theta }{5}$
C) $8=r(1+3\cos \theta )$

• A. $B,C,A$
• B. $B,A,C$
• C. $A,B,C$
• D. $A,C,B$

Answer 1

The correct option is C $A,B,C$

General equation of conic in polar form is $\frac{l}{r}=1\pm e\cos \theta$
A) $r(4+\cos \theta )=8\Rightarrow \frac{2}{r}=1+\frac{1}{4}\cos \theta \Rightarrow e=\frac{1}{4}$
B) $\frac{1}{r}=\frac{3}{5}-\frac{3\cos \theta }{5}\Rightarrow \frac{5/3}{r}=1-\cos \theta \Rightarrow e=1$
C) $8=r(1+3\cos \theta )\Rightarrow \frac{8}{r}=1+3\cos \theta \Rightarrow e=3$