Question

Observe the following lists
The polar equations of the curves

LIST-I	LIST-II
A) $x^2+y^2=a^2$	1. $r\cos 2\theta =2a\sin \theta$
B) $x^2-y^2=2ay$ is	2. $r=2a\cos \theta$
C) $x^2+y^2=4x+3y$	3. $r=a$
D) $x^2+y^2=2ax$	4. $r=4\cos \theta +3\sin \theta$

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

• A. $3,1,4,2$
• B. $3,1,2,4$
• C. $3,2,1,4$
• D. $4,1,2,3$

Answer 1

The correct option is A $3,1,4,2$

put $x=r\cos \theta$ and $y=r\sin \theta$
A) $x^2+y^2=a^2$
$\Rightarrow r^2=a^2$
$\Rightarrow r=a$
B) $x^2-y^2=2ay$
$r^2({\cos }^2\theta -{\sin }^2\theta )=2ar\sin \theta$
$\Rightarrow r\cos 2\theta =2a\sin \theta$

C) $x^2+y^2=4x+3y$
$r^2=4r\cos \theta +3r\sin \theta$
$r=4\cos \theta +3\sin \theta$
D) $x^2+y^2=2ax$
$r^2=2ar\sin \theta$
$r=2a\sin \theta$
Ans: A