TS EAMCET · Maths · Circle
If the length of the chord \(2 x+3 y+\mathrm{k}=0\) of the circle \(x^2+y^2-2 x+4 y-11=0\) is \(2 \sqrt{3}\), then the sum of all possible values of \(k\) is
- A \(26\)
- B \(8\)
- C \(13\)
- D \(4\)
Answer & Solution
Correct Answer
(B) \(8\)
Step-by-step Solution
Detailed explanation
Center of circle \(C = (1, -2)\). Radius \(r = \sqrt{(-1)^2 + (2)^2 - (-11)} = \sqrt{1+4+11} = \sqrt{16} = 4\). Distance from center to chord \(d = \frac{|2(1)+3(-2)+k|}{\sqrt{2^2+3^2}} = \frac{|k-4|}{\sqrt{13}}\). Chord length formula:…
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