Show that a tangent to an ellipse whose tangent intercepted by the axes is the shortest, is divided at the point of tangency into two parts respectively, is equal to the semi-axes of the ellipse.

Prove that the segment of tangent to xy=c^(2) intercepted between the axes is bisected at the point at contact .

For the curve x y=c , prove that the portion of the tangent intercepted between the coordinate axes is bisected at the point of contact.

For the curve x y=c , prove that the portion of the tangent intercepted between the coordinate axes is bisected at the point of contact.

Find the tangent of the angle between the lines whose intercepts on the axes are respectively a ,-b and b ,-a

Find the tangent of the angle between the lines whose intercepts on the axes are respectively a,−b and b,−a

If the normal at any point P on the ellipse cuts the major and minor axes in G and g respectively and C be the centre of the ellipse, then

Prove that if any tangent to the ellipse is cut by the tangents at the endpoints of the major axis at Ta n dT ' , then the circle whose diameter is T T ' will pass through the foci of the ellipse.

The equations of the tangents to the ellipse 3x^(2)+y^(2)=3 making equal intercepts on the axes are

If theta is the difference of the eccentric angles of two points on an ellipse, the tangents at which are at right angles. Prove that a b sintheta=d_1d_2 , where d_1,d_2 are the semi diameters parallel to the tangents at the points and a,b are the semi-axes of the ellipse.

Prove that the portion of the tangent to an ellipse intercepted between the ellipse and the directrix subtends a right angle at the corresponding focus.