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TS EAMCET · Maths · Circle

The centre of the circle passing through the point \((1,1)\) and orthogonal to the circles \(x^2+y^2+3 x-5 y+7=0\) and \(x^2+y^2-6 x-10 y+9=0\) is

  1. A \(\left(-\frac{19}{52}, \frac{71}{52}\right)\)
  2. B \(\left(\frac{19}{52},-\frac{55}{52}\right)\)
  3. C \(\left(-\frac{55}{52}, \frac{19}{52}\right)\)
  4. D \(\left(-\frac{19}{52}, \frac{55}{52}\right)\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(\left(-\frac{19}{52}, \frac{55}{52}\right)\)

Step-by-step Solution

Detailed explanation

Let the equation of circle is \(x^2+y^2+2 g x+2 f y+c=0\) \(\because\) Circle (i) passes through point \((1,1)\), so \(\begin{aligned} & 1+1+2 g+2 f+c=0 \\ & \Rightarrow \quad 2 g+2 f+c+2=0 \\ & \end{aligned}\) \(\because\) Circle Eq. (i) is orthogonal to circles…