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AP EAMCET · Maths · Circle

If the chord joining the points \((1,2)\) and \((2,-1)\) on a circle subtends an angle of \(\frac{\pi}{4}\) at any point on its circumference then the equation of such a circle is

  1. A \(x^2+y^2+6 x-2 y+5=0\)
  2. B \(x^2+y^2-6 x-2 y+5=0\)
  3. C \(x^2+y^2-6 x+2 y+5=0\)
  4. D \(x^2+y^2+6 x+2 y+5=0\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(x^2+y^2-6 x-2 y+5=0\)

Step-by-step Solution

Detailed explanation

\((x-x_1)(x-x_2) + (y-y_1)(y-y_2) \pm \cot \theta [(y-y_1)(x_2-x_1) - (x-x_1)(y_2-y_1)] = 0\) \((x-1)(x-2) + (y-2)(y+1) \pm \cot(\frac{\pi}{4}) [(y-2)(2-1) - (x-1)(-1-2)] = 0\) \((x^2-3x+2) + (y^2-y-2) \pm 1 \cdot [(y-2) - (-3x+3)] = 0\) \(x^2+y^2-3x-y \pm [3x+y-5] = 0\)…