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

Length of common tangents to the hyperbolas x^2/a^2-y^2/b^2=1 and y^2/a^2-x^2/b^2=1 is

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

Find the length of latus rectum L of ellipse (x^(2))/(A^(2)) + (y^(2))/(9) = 1, (A^2) gt 9) where A^2 is the area enclosed by quadrilateral formed by joining the focii of hyperbola (x^(2))/(16) - (y^(2))/(9) = 1 and its conjugate hyperbola

Find the length of latus rectum L of ellipse (x^(2))/(A^(2)) + (y^(2))/(9) = 1, (A^2) gt 9) where A^2 is the area enclosed by quadrilateral formed by joining the focii of hyperbola (x^(2))/(16) - (y^(2))/(9) = 1 and its conjugate hyperbola

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 Pa n dQ , respectively, then prove that normal at Pa n dQ meet on the x-axis.

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 Pa n dQ , respectively, then prove that normal at Pa n dQ meet on the x-axis.

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.

The condition that the line x cos alpha + y sin alpha =p to be a tangent to the hyperbola x^(2)//a^(2) -y^(2)//b^(2) =1 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.

The equations (s) to common tangent (s) to the two hyperbola x^(2)/a^(2) - y^(2)/b^(2) = 1 " and " y^(2)/a^(2) - x^(2)/b^(2) = 1 is /are