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The length of the common chord of the circles $x^{2} + y^{2} + 4 x + 1 = 0$ and $x^{2} + y^{2} + 4 y - 1 = 0,$ is

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Given circles intersect orthogonally. So, the length of their common chord is l=2r1r2r12+r22,where r1 and r2 are the radii of the given circles.Here, r1=5 and r2=3. ∴ l=2155+3=152..

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The length of the common chord of the circles x2+y2+4x+1=0 and x2+y2+4y−1=0, is

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The length of the common chord of the circles $x^{2} + y^{2} + 4 x + 1 = 0$ and $x^{2} + y^{2} + 4 y - 1 = 0,$ is