UPSC NDA I 2025 Mathematics Paper

Given two diameters of the circle are along the lines x+y=0 and x−y=0. The center of the circle is at their intersection.
We have,
x−y=0⇒x=y
Substitute into x+y=0 :
x+x=0⇒2x=0⇒x=0,y=0
Thus, the center is (0,0).
Also radius,
r=‌

10

2

=5
the equation of the circle with center (0,0) and radius 5 is
x2+y2=52=25