TS EAMCET · Maths · Circle
The centre of the circle touching the circles \(x^2+y^2-4 x-6 y-12=0\), \(x^2+y^2+6 x+18 y+26=0\) at their point of contact and passing through the point \((1,-1)\) is
- A \(\left(\frac{1}{3},-1\right)\)
- B \(\left(\frac{1}{5}, \frac{6}{5}\right)\)
- C \(\left(\frac{1}{2}, 1\right)\)
- D \(\left(-\frac{1}{4},-\frac{1}{2}\right)\)
Answer & Solution
Correct Answer
(A) \(\left(\frac{1}{3},-1\right)\)
Step-by-step Solution
Detailed explanation
\(S_1: x^2+y^2-4 x-6 y-12=0\) \(S_2: x^2+y^2+6 x+18 y+26=0\) The equation of the required circle is \(S_1 + \lambda S_2 = 0\): \((x^2+y^2-4 x-6 y-12) + \lambda (x^2+y^2+6 x+18 y+26) = 0\) Passes through \((1,-1)\): \((1+1-4-6-12) + \lambda (1+1+6-18+26) = 0\)…
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