AP EAMCET Engineering 2018 Apr 24 Shift 1 Paper

Let the equation of the circle is
x2+y2+2gx+2fy+c=0
Centre is (−g,−f)
since the circle passes through the point (0,2) .
4+0+4g+0+c=0
4+4g+c=0
And circle also touches the X-axis.
g2=c
Substitute the values
4+4g+g2=0
(g+2)2=0
g=−2
and c=4
This circle also cuts the circle x2+y2−2x−2y−2=0 orthogonally
2g1g2+2f1f2=c1+c2
2(−2)(−1)+2f(−1)=4−2
f=1
Hence the coordinate of the centre of the circle is (2,-1) .