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AP EAMCET · Maths · Circle

If the equation of the circle passing through the point \((8,8)\) and having the lines \(x+2 y-2=0\) and \(2 x+3 y-1=0\) as its diameters is \(x^2+y^2+p x+q y+r=0\), then \(p^2+q^2+r=\)

  1. A \(244\)
  2. B \(100\)
  3. C \(-44\)
  4. D \(44\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(-44\)

Step-by-step Solution

Detailed explanation

Solving \(x+2y-2=0\) and \(2x+3y-1=0\): \((x,y) = (-4,3)\). Center of circle: \((-4,3)\). Radius squared \(R^2 = (8-(-4))^2+(8-3)^2 = 12^2+5^2 = 144+25 = 169\). Equation of circle: \((x+4)^2+(y-3)^2 = 169\). \(x^2+8x+16+y^2-6y+9 = 169\). \(x^2+y^2+8x-6y-144 = 0\). Comparing with…