S1:x2+y2−4x+6y−10=0 ...(i) S2:x2+y2+2x−6y+2=0 ...(ii) Equation of radical axis S1−S2=0 ⇒(x2+y2−4x+6y−10)−(x2+y2+2x−6y+2)=0 ⇒6x−12y+12=0 ⇒x−2y+2=0 ...(iii) Given that Eq. (iii) cut the circle (i), Using Eq. (iii) in Eq. (i) as, x=2y−2 (2y−2)2+y2−4(2y−2)+6y−10=0 ⇒4y2+4−8y+y2−8y+8+6y−10=0 ⇒5y2−10y+2=0 ⇒y=
10±√100−40
10
=
5±√15
5
⇒x=2(
5±√15
5
) Thus, Eq. (iii) cuts S1 at two real and distinct points.