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AP EAMCET · Maths · Circle

If the length of the chord \(2 x+3 y+k=0\) of the circle \(x^2+y^2-6 x-8 y+9=0\) is \(2 \sqrt{3}\), then one of the values of \(\mathrm{k}\) is

  1. A 31
  2. B 5
  3. C \(-5\)
  4. D \(-13\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(-5\)

Step-by-step Solution

Detailed explanation

The given equation of circle is \(x^2+y^2-6 x-8 y+9=0\) Its centre is \(C=(3,4)\) and Radius \(R=\sqrt{9+16-9} \Rightarrow R=\sqrt{16}=4\) \(\because A B=2 \sqrt{3}\) \(\Rightarrow \quad A M=\frac{A B}{2}=\frac{2 \sqrt{3}}{2}=\sqrt{3}\) And…