Equation of conjugate hyperbola w.r.t `(x^(2))/(a^(2))-(y^(2))/(b^(2))=1` is

If any line perpendicular to the transverse axis cuts the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 and the conjugate hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=-1 at points P and Q, respectively,then prove that normal at P and Q meet on the x-axis.

The auxiliary equation of circle of hyperbola (x ^(2))/(a ^(2)) - (y^(2))/(b ^(2)) =1, is

Show that the equation of the tangent to the hyperbola (x^(2))/(a^(2)) - (y^(2))/(b^(2)) = 1 " at " (x_(1), y_(1)) " is " ("xx"_(1))/(a^(2)) - (yy_(1))/(b^(2)) = 1

If the ratio of transverse and conjugate axis of the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 passing through the point (1,1) is (1)/(3), then its equation is

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

The sides AC and AB of a o+ABC touch the conjugate hyperbola of the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1. If the vertex A lies on the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1, then the side BC must touch parabola (b) circle hyperbola (d) ellipse

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

Eccentricity of a hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 is " (sqrt(41))/(5), the ratio of length of transverse axis to the conjugate axis is

Ecceptricity of the hyperbola conjugate to the hyperbola (x^(2))/(4)-(y^(2))/(12)=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