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TS EAMCET · Maths · Circle

\((1, k)\) is a point on the circle passing through the points \((-1,1),(0,-1)\) and \((1,0)\). If \(k \neq 0\), then \(k=\)

  1. A \(\frac{1}{2}\)
  2. B \(\frac{1}{3}\)
  3. C \(-\frac{1}{3}\)
  4. D \(-\frac{1}{2}\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(\frac{1}{3}\)

Step-by-step Solution

Detailed explanation

Let the equation of the circle be \(x^2+y^2+2 g x+2 f y+C=0\) \((-1,1),(0,-1)\) and \((1,0)\) lie on this circle. \(\begin{aligned} & 1-2 f+C=0...(i) \\ & 1+2 g+C=0...(ii) \\ & 1+1-2 g+2 f+C=0 \\ & \Rightarrow 2 g-2 f-C=2...(iii) \end{aligned}\) Solving (i), (ii) and (iii),…