UPSC NDA Math Model Paper 10

Given the circle touches the x and y axis, i.e., x and y axis are tangent to the circle.
Equation of the x-axis is y = 0
Radius is perpendicular distance of centre (-2, -2) from the tangent (y = 0)
Radius r=|

ax1+by1+c

√a2+b2

|
⇒r=|

0×(−2)+1×(−2)+0

√02+12

|
⇒r=|−2|=2
Equation of circle having centre (-2, -2) and radius r = 2 is:
(x−h)2+(y−k)2=R2
⇒(x−(−2))2+(y−(−2))2=22
⇒x2+y2+4x+4y+8=4
⇒x2+y2+4x+4y+4=0