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

If e and e' are the eccentricities of the hyperbola x^(2)/a^(2)-y^(2)/b^(2)=1 and its conjugate hyperbola,the value of 1/e^(2)+1/e^prime2 is

Show that the line y=2x-4 is a tangent to the hyperbola (x^(2))/(16)-(y^(2))/(48)=1. Find its point of contact.

Find the common tangents to the hyperbola x^(2)-2y^(2)=4 and the circle x^(2)+y^(2)=1

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.

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

Prove that the line y = x - 1 cannot be a normal of the hyperbola x^(2) - y^(2) = 1 .

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 e and e\' are the eccentricities of the hyperbola x^2/a^2 - y^2/b^2 = 1 and its conjugate hyperbola, prove that 1/e^2 + 1+e\'^2 = 1

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.

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