If PQ is a double ordinate of the hyperbola `(x^(2))/(a^(2))-(y^(2))/(b^(2))=1`
such that OPQ is an equilateral triangle, O being the centre of the hyperbola, then find range of the eccentricity (e) of the hyperbola.

If P Q is a double ordinate of the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 such that O P Q is an equilateral triangle, O being the center of the hyperbola, then find the range of the eccentricity e of the hyperbola.

If the latus rectum of a hyperbola forms an equilateral triangle with the vertex at the center of the hyperbola ,then find the eccentricity of the hyperbola.

The eccentricity of the hyperbola (y^(2))/(9)-(x^(2))/(25)=1 is …………………

If e is the eccentricity of the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 and theta is the angle between the asymptotes, then cos.(theta)/(2) is equal to

If it is possible to draw the tangent to the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 having slope 2, then find its range of eccentricity.

If the chords of contact of tangents from two points (-4,2) and (2,1) to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 are at right angle, then find then find the eccentricity of the hyperbola.

A variable chord of the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1,(b > a), subtends a right angle at the center of the hyperbola if this chord touches. a fixed circle concentric with the hyperbola a fixed ellipse concentric with the hyperbola a fixed hyperbola concentric with the hyperbola a fixed parabola having vertex at (0, 0).

The tangent at P on the hyperbola (x^(2))/(a^(2)) -(y^(2))/(b^(2))=1 meets one of the asymptote in Q. Then the locus of the mid-point of PQ is

Locus of perpendicular from center upon normal to the hyperbola (x^(2))/(a^(2)) -(y^(2))/(b^(2)) =1 is

The number of normals to the hyperbola x^(2)/a^(2) - y^(2)/b^(2) = 1 from an external point is _______