UPSC NDA Math Model Paper 6

Given diameter = 8
⇒ Radius = 4
Also diameters equations:
y + 2x - 5 = 0 ...(i)
2y + 3x - 8 = 0 ...(ii)
Substracting 2 × (i) from (ii)
-x + 2 = 0
x = 2
Putting back in (i)
y + 2 × 2 - 5 = 0
y = 1
So center is (2, 1) and radius 4
The equation of circle:
(x−2)2+(y−1)2=42(x−2)2 +(y−1)2=42
⇒x2+4−4x+y2+1−2y=16x2+4 −4x+y2+1−2y=16
⇒x2+y2−4x−2y−11=0
x2+y2−4x−2y−11=0