AP EAPCET 20-Aug-2021 Shift 2 Paper

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.