Let two circles with radii r1 and r2 have their centers at a distance of -2r1-r2 -If r1 and r2 are roots of the equation x2 - 2- - -x - -2 - -2-0- then the relation between - and - for which the two circles are orthogonal is

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Rectangular Hyperbola

Let two circl...

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Let two circles with radii $r_{1}$ and $r_{2}$ have their centers at a distance of $\sqrt{2} (r_{1} - r_{2})$ .
If $r_{1}$ and $r_{2}$ are roots of the equation $x^{2} - 2 (α + β) x + α^{2} + β^{2} = 0$ , then the relation between $α$ and $β$ for which the two circles are orthogonal is

α^{2} + β^{2} = 4 α β

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(α + β)^{2} = 4 α β

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α^{2} + β^{2} = α β

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α^{2} - β^{2} = 4 α β

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