Question

The parametric equation $x=\frac{2a(1-t^2)}{1+t^2}$ and $y=\frac{4at}{1+t^2}$ represent a circle of radius

• A. $\frac{a}{2}$
• B. $2a$
• C. $3a$
• D. $4a$

Answer 1

The correct option is B $2a$

$x=\frac{2a(1-t^2)}{1+t^2}$ and $y=\frac{4at}{1+t^2}$
$let,t=\tan \theta$
$x=2a\left(\frac{1-{\tan }^2\theta }{1+{\tan }^2\theta }\right)$ $\Rightarrow x=2a\cos 2\theta$
$y=\frac{4a\tan \theta }{1+{\tan }^2\theta }$ $\Rightarrow y=2a\sin 2\theta$
$\therefore \frac{x^2}{4a^2}+\frac{y^2}{4a^2}=1$
$x^2+y^2=4a^2$
So, the radius of circle is $2a$.