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 \(p^2+q^2+r=\)
- A \(244\)
- B \(100\)
- C \(-44\)
- D \(44\)
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…
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