A tangent drawn to hyperbola `(x^(2))/(a^(2))-(y^(2))/(b^(2)) =1`at `P((pi)/(6))` forms a triangle of area `3a^(2)` square units, with coordinate axes, then the squae of its eccentricity is equal to

A tangent drawn to hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 at P((pi)/(6)) froms a triangle of area 3a^(2) square units,with the coordinate axes,then the square of its eccentricity is (A) 15(B)24(C)17 (D) 14

A tangent drawn to the hyperbola (x^2)/(a^2) - (y^2)/(b^2) = 1 at P(a "sec" pi/6, b tan pi/6) form a triangle of area 3a^2 sq. units with the coordinate axes. The eccentricity of the conjugate hyperbola of (x^2)/(a^2) - (y^2)/(b^2) = 1 is

From a point P, two tangents PA and PB are drawn to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 . If the product of the slopes of these tangents is 1, then the locus of P is a conic whose eccentricity is equal to

The locus of the point which is such that the chord of contact of tangents drawn from it to the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 forms a triangle of constant area with the coordinate axes is a straight line (b) a hyperbola an ellipse (d) a circle

The tangent at the vertex of the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 meets its conjugate hyperbola at the point whose coordinates are

From a point P, two tangents PA and PB are drawn to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 . If these tangents cut the coordinates axes at 4 concyclic points, then the locus of P is

The asymptote of the hyperbola (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 form with ans tangen to the hyperbola triangle whose area is a^(2)tan lambda in magnitude then its eccentricity is: (a) sec lambda(b)cos ec lambda(c)sec^(2)lambda(d)cos ec^(2)lambda

If normal to hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 drawn at an extremity of its latus-rectum has slope equal to the slope of line which meets hyperbola only once,then the eccentricity of hyperbola is