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TS EAMCET · Maths · Circle

The power of a point \((2,-1)\) with respect to a circle C of radius 4 is 9. The centre of the circle C lies on the line \(x+y=0\) and in the \(2^{\text {nd }}\) quadrant. If \((\alpha, \beta)\) is the centre of the circle C, then \(\beta-\alpha=\)

  1. A \(-4\)
  2. B \(-10\)
  3. C \(4\)
  4. D \(10\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(4\)

Step-by-step Solution

Detailed explanation

\((2-\alpha)^2 + (-1-\beta)^2 - 4^2 = 9\) \((2-\alpha)^2 + (1+\beta)^2 = 25\) \(\alpha + \beta = 0 \Rightarrow \beta = -\alpha\) \((2-\alpha)^2 + (1-\alpha)^2 = 25\) \(4 - 4\alpha + \alpha^2 + 1 - 2\alpha + \alpha^2 = 25\) \(2\alpha^2 - 6\alpha + 5 = 25\)…