Number of Common Tangents to Two Circles in Different Conditions
The common ch...
Question
The common chord of the circle x2+y2+6x+8y−7=0 and another circle passing through origin, which touches the line y = x, always passes through the point (α,β), then |α−β|=___
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Solution
x2+y2+6x+8y−7=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)