UPSC NDA I 2015 Mathematics Solved Paper

Consider the parametric equation of x and y.
x=

a(1−t2)

1+t2

y=

2at

1+t2

Let
t=tanθ
Hence the above parametric equations,simplifies to
x=

a(1−tan2θ)

1+tanθ

=acos2θ
y=

2atanθ

1+tan2θ

=asin2θ
Hence
x=acos2θ
y=asin2θ
Squaring and adding the above equations, we get
x2+y2=a2(cos22θ+sin22θ)
x2+y2=a2
This represents the equation of a circle centered at the origin with a radius of ‘a’ units.