Question

The locus of the curve whose perametric equations are $x=a\left(\frac{1-t^2}{1+t^2}\right)$ and $y=\frac{2at}{1+t^2}$, where $t$ being a parameter is

• A. a circle with a radius of $a$ units
• B. a circle passing through origin
• C. pair of lines passsing through $(a,a)$
• D. pair of lines passsing through $(0,0)$

Answer 1

The correct option is A a circle with a radius of $a$ units

Given, $x=a\left(\frac{1-t^2}{1+t^2}\right)$ and $y=\frac{2at}{1+t^2}$
$\Rightarrow x^2+y^2=a^2\left(\frac{(1-t^2{)}^2+4t^2}{(1+t^2{)}^2}\right)$
$\therefore x^2+y^2=a^2$
Which represents a circle of radius $a\text{units}.$