Question

The cartesian equation of $r^2\cos 2\theta =a^2$ is

• A. $x-y=a^2$
• B. $x+y=a^2$
• C. $x^2+y^2=a^2$
• D. $x^2-y^2=a^2$

Answer 1

The correct option is D $x^2-y^2=a^2$

The given equation
$r^2\cos 2\theta =a^2$
$\Rightarrow r^2({\cos }^2\theta -{\sin }^2\theta )=a^2$
Substituting $x=r\cos \theta ,y=r\sin \theta$
We get cartesian equation
$x^2-y^2=a^2$
Hence, option 'D' is correct.