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If x^(2) + y^(2) - 4x - 2y + 5 = 0 and x^(2 + y^(2) - 6x - 4y = 0 are membes of a coaxal system of circles then centre of a point circle in the systems is |
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Answer» (-5, -6) and `S^(1) -= x^(2) + y^(2) - 6x - 4y - 3 = 0` Equation of coaxial system of circles is `S + lambda L - 0` `L = S - S^(1) = 0` `implies 2X + 2y + 8 = 0` `implies x + y + 4 = 0` `implies x^(2) + y^(2) - 4x - 2y + 5 + lambda x + lambda y +4 lambda = 0` `implies x^(2) + y^(2) + x (lambda - 4) + y (lambda - 2) + (5 + 4 lambda) = 0` centre, `C = [(4 - lambda)/(2), (2 - lambda)/(2)]` and radius, r = 0 `implies (16 - 8lambda + lambda^(2) + 4 - 4 lambda + lambda^(2) - 20 - 16 lambda)/(4) = 0` `implies 2 lambda^(2) - 28 lambda = 0` `implies lambda (lambda - 14) = 0` `implies lambda 0, 14` `implies` centre `C = ((4)/(2), (2)/(2))` (or) `((-10)/(2), (-12)/(2))` `:. C = (2,1)` (or) (-5, -6) |
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