AP EAMCET Engineering 21 Sep 2020 Shift 2 Paper

(b) The radical axis of any two circles is perpendicular to the line joining their centres.
Let, the equation of two circles are
x2+y2+2g1x+2f1y+c1=0 and
x2+y2+2g2x+2f2y+c2=0
The equation of the radical axis is
2(g1−g2)x+2(f1−f2)y+(c1−c2)=0‌‌.....(i)
∵ Slope of line (i) is −‌

g1−g2

f1−f2

=m1‌‌......let(ii)
and slope line joining centres of the circles is
‌

f1−f2

g1−g2

=m2‌‌(let)
∵‌‌m1m2=−‌

g1−g2

f1−f2

×‌

f1−f2

g1−g2

=−1