If `ax+by=1` is tangent to the hyperbola `x^2/a^2-y^2/b^2=1` then `a^2-b^2=`

If ax+by=1 is tangent to the hyperbola (x^(2))/(a_(1)^(2))-(y^(2))/(b^(2))=1, then a^(2)-b^(2) is equal to (A)(1)/(a^(2)e^(2))(B)a^(2)e^(2)(C)b^(2)e^(2)(D) none of these

The line 2x+y=1 is tangent to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1. If this line passes through the point of intersection of the nearest directrix and the x-axis,then the eccentricity of the hyperbola is

The line 2x+y=1 is tangent to the hyperbla (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 . If this line passes through the point of intersection of the nearest directrix and the x -axis, then the eccentricity of the hyperbola is

Statement 1 : If from any point P(x_1, y_1) on the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=-1 , tangents are drawn to the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1, then the corresponding chord of contact lies on an other branch of the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=-1 Statement 2 : From any point outside the hyperbola, two tangents can be drawn to the hyperbola.

The product of the perpendicular from two foci on any tangent to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 is (A)a^(2)(B)((b)/(a))^(2)(C)((a)/(b))^(2) (D) b^(2)

Find the area of the triangle formed by any tangent to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 with its asymptotes.

If the slope of a tangent to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 is 2sqrt(2) then the eccentricity e of the hyperbola lies in the interval

Show that there cannot be any common tangent to the hyperbola x^(2)/a^(2) - y^(2)/b^(2) = 1 and its conjugate hyperbola.