TS EAMCET · Maths · Circle
If a circle passing through the point \((1,1)\) cuts the circles \(x^2+y^2+4 x-5=0\) and \(x^2+y^2-4 y+3=0\) orthogonally then the center of that circle is
- A \(\left(\frac{3}{4}, \frac{5}{4}\right)\)
- B \(\left(\frac{3}{2}, \frac{5}{2}\right)\)
- C \(\left(-\frac{3}{2},-\frac{5}{2}\right)\)
- D \(\left(-\frac{3}{4},-\frac{5}{2}\right)\)
Answer & Solution
Correct Answer
(A) \(\left(\frac{3}{4}, \frac{5}{4}\right)\)
Step-by-step Solution
Detailed explanation
Let eq. of circle be \(x^2+y^2+2 g x+2 f y+C=0 \quad ...\mathrm{(i)}\) (i) passes through \((1,1)\) \(\Rightarrow 2 g+2 f+C=-2 \quad ...\mathrm{(ii)}\) Condition for orthogonality \(2 g_1 g_2+2 f_1 f_2=C_1+C_2\) With circle \(x^2+y^2+4 x-5=0\)…
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