TS EAMCET 11-Sep-2020 Shift 2 Solved Paper

Given circle,
s1:x2+y2−8x−6y+21=0
and S2:x2+y2−2y−15=0
Circle S1: Centre C1(4,3), radius r1=√16+9−21=2
S2: Centre C2(0,1), radius r2=√1+15=4
Now ‌‌C1C2=√42+22=√20
∴C1C2<r1+r2⇒ circle C1 and C2 put with other.Let point of intersection of tangent on the circle S1 and S2 is P.
Now, point P divide line joining C2C1 in the ratio of their radii externally
∴‌‌‌

C2P

C1P

=‌

r2

r1

⇒‌

C2P

C1P

=‌

4

2

=‌

2

1

∴ By using external division formula
=(‌

m1n2−m2n1

m1−m2

,‌

m1y2−m2y1

m1−m2

)