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 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 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

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

If the eccentricity of the hyperbola (x^(2))/(16)-(y^(2))/(b^(2))=-1 is (5)/(4) , then b^(2) is equal to

If the tangent drawn to the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 at any point P meets the coordinate axes at the points A and B respectively. If the rectangle OACB (O being the origin) is completed, where C lies on (x^2)/(a^2)-(y^2)/(b^2)=lambda . Then, the value of lambda is:

The latus rectum of a hyperbola (x^(2))/( 16) -(y^(2))/( p) =1 is 4(1)/(2) .Its eccentricity e=

If the latus rectum of the hyperbola (x^(2))/(16)-(y^(2))/(b^(2))=1 is (9)/(2) , then its eccentricity, is

Tangent at a point on the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 is drawn which cuts the coordinates axes at A and B the minimum area of the triangle OAB is ( O being origin )

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