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)) 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 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

A tangent to a hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 intercepts a length of unity from each of the coordinate axes,then the point (a,b) lies on rectangular hyperbola

Consider the hyperbola x^(2)/a^(2) - y^(2)/b^(2) = 1 . Area of the triangle formed by the asymptotes and the tangent drawn to it at (a, 0) is

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

If a line passes through the point (2,2) and encloses a triangle of area A square units with the coordinate axes , then the intercepts made by the line on the coordinate axes are the roots of the equations

If the straight line a x+c y=2b , where a , b , c >0, makes a triangle of area 2 sq. units with the coordinate axes, then (a)a , b , c are in GP (b)a, -b; c are in GP (c)a ,2b ,c are in GP (d) a ,-2b ,c are in GP