Question

The locus of centres of all circle passing through (1,2) and cutting x^2+y^2=16 orthogonally is

Answer 1

Let the equation of a circle be
Xv2+yv2+2gx+2fy+c=0
This circle is orthogonal to xv2+yv2-16=0
Then c-16=0
Therefore c=16
The circle is passing through (1,2)
1+4+2g+4f+16=0
2g+4f+21=0
The locus of the centre is
-2x-4y+21=0
2x+4y-21=0