Recent questions and answers in Maths

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A double ordinate \(P Q\) of the hyperbola \(\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1\) is such that \(\Delta O P Q\) is equilateral, \(O\) being the centre of the hyperbola. Then the eccentricity e satisfies the relation

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The length of conjugate axis of a hyperbola is greater than the length of transverse axis. Then the eccentricity e is,

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A chord \(A B\) is drawn from the point \(A(0,3)\) on the circle \(x^{2}+4 x+(y-3)^{2}=0\), and is extended to \(M\) such that \(\mathrm{AM}=2 \mathrm{AB} .\) The locus of \(\mathrm{M}\) is

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