Let F_1, F_2 be foci of hyperbola \frac{{x}^2}{{a}^2}-\frac{{y}^2}{{b}^2}=1, a>0, b>0, and let O be the origin. Let M be an arbitrary point on curve C and above X-axis and H be a
point on MF_1 such that MF_2\perp{{F}}_1{{F}}_2, MF_1\perp{{O}}{{H}}, |OH|=\lambda |OF_2| with \lambda \in(2/5, 3/5), then the range of the eccentricity e is
The locus of the intersection of the two lines \sqrt{3} x-y=4k\sqrt{3} and k(\sqrt{3}x+y)=4\sqrt{3}, for different
values of k, is a hyperbola. The eccentricity of the hyperbola is:
If PQ is a double ordinate of the hyperbola \frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1 such that OPQ is an equilateral triangle,
where O is the centre of the hyperbola, then which of the following is true?