Question

Observe the following lists

LIST-I	LIST-II
A) $r=a\cos \theta$	1. ellipse
B) $\frac{1}{r}=\frac{1}{8}+\frac{3}{8}\cos \theta$	2. circle
C) $\frac{4}{r}=1+\frac{3}{4}\cos \theta$	3. parabola
D) $\frac{l}{r}=1+\cos \theta$	4. hyperbola

The correct match of LIST-I from LIST-II is
A B C D

• A. $2431$
• B. $2413$
• C. $1324$
• D. $1342$

Answer 1

The correct option is B $2413$

We know $x=r\cos \theta ,y=r\sin \theta ,r^2=x^2+y^2$
A. $r=a\cos \theta =\frac{ax}{r}\Rightarrow r^2=ax\Rightarrow x^2+y^2-ax=0\Rightarrow$ circle
Also we know standard form of conic is $\frac{l}{r}=1+e\cos \theta$

B. $\frac{1}{r}=\frac{1}{8}+\frac{3}{8}\cos \theta \Rightarrow \frac{8}{r}=1+3\cos \theta \Rightarrow e=3>1\Rightarrow$Hyperbola

C. $\frac{4}{r}=1+\frac{3}{4}\cos \theta \Rightarrow e=\frac{3}{4}<1\Rightarrow$Ellipse

D. $\frac{l}{r}=1+\cos \theta \Rightarrow e=1\Rightarrow$Parabola