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Question

The common chord of the circle x2+y2+6x+8y7=0 and another circle passing through origin, which touches the line y = x, always passes through the point (α,β), then |αβ|=___
 


Solution

x2+y2+6x+8y7=0  ----------------------  (1)
x2+y2+2gx+2gy=0  ----------------------  (2)
Equ of common chord is 
2(g - 3) x + 2 (-g  -4) y + 7 = 0 
(-6x-8y+7)+g (2x-2y)=0
Always P. T. (12,12)

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