For the hyperbola `(x^(2))/(a^(2))-(y^(2))/(b^(2))=1`, distance between the foci is 10 units. Form the point `(2, sqrt3)`, perpendicular tangents are drawn to the hyperbola, then the value of `|(b)/(a)|` is

For hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1, let n be the number of points on the plane through which perpendicular tangents are drawn.

Prove that the part of the tangent at any point of the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 intercepted between the point of contact and the transvers axis is a harmonic mean between the lengths of the perpendiculars drawn from the foci on the normal at the same point.

The tangent at a point P on the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 passes through the point (0,-b) and the normal at P passes through the point (2a sqrt(2),0). Then the eccentricity of the hyperbola is 2( b) sqrt(2)(c)3(d)sqrt(3)

If the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2)) passes through the points (3sqrt2, 2) and (6, 2sqrt(3)) , then find the value of e i.e., eccentricity of the given hyperbola.

Find the points on the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))= 2 from which two perpendicular tangents can be drawn to the circle x^(2) + y^(2) = a^(2)

The locus of the point of intersection of perpendicular tangents to the hyperbola (x^(2))/(3)-(y^(2))/(1)=1 , is

Find the equations of the tangent and normal to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 at the point

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 hyperbola (y^(2))/(a^(2))-(x^(2))/(b^(2)) =1 passes through the points (0, -2) and (sqrt(3). 4) . Find the value of e i.e., the eccentricity of the given hyperbola.