TS EAMCET 4-Aug-2021 Shift 1 Question Paper

Let S≡(x−2)2+(y−3)2=25
Centre C1(2,3) and radius r1=5
and S′≡x2+y2−‌

40

25

x−‌

70

25

y−‌

160

25

=0
Centre C2(‌

4

5

,‌

7

5

) and radius r2=3
If circle S and S′ with centre C1(x1,y1) and C2(x2,y2) and having radius r1 and r2 respectively touches
each other internally. Then, coordinate of point of contact is (‌

r1x2−r2x1

r1−r2

,‌

r1y2−r2y1

r1−r2

)
Putting the values, we have
(α,β)=(‌

5× 4 5 −3×2

5−3

,‌

5× 7 5 −3×3

5−3

)=(−1,−1)
∴α+β=(−1)+(−1)=−2