Question

Consider the parametric equation
$x=\frac{a(1-t^2)}{1+t^2},y=\frac{2at}{1+t^2}$.

What does the equation represent?

• A. It represents a circle of diameter $a$
• B. It represents a circle of radius $a$
• C. It represents a parabola
• D. None of the above

Answer 1

The correct option is B It represents a circle of radius $a$

$x=\frac{a(1-t^2)}{1+t^2},y=\frac{2at}{1+t^2}$

Let $t=\tan \theta$

$\Rightarrow x=a\sin 2\theta ,y=a\cos 2\theta \Rightarrow x^2+y^2=a^2$

It represents a circle of radius $a$.