TS EAMCET 10-Sep-2020 Shift 1 Solved Paper

We have
S1:x2+y2+kx−4y−1=0
=x2+y2−‌

14

3

x+‌

23

3

y−5=0
Since, S1 and S2 are orthogonal
⇒‌‌7k=−28⇒k=−4
∴‌‌S1:x2+y2−4x−4y−1=0
S2:x2+y2−‌

14

3

x+‌

23

3

y−5=0
Equation of circle passing through intersection of S1 and S2 is
Since above circle passes through (−1,−1), so
9−6λ=0⇒λ=‌

3

2

∴ Equation of required circle is