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.

Find the tangent of the angle between the lines whose intercepts on the axes are respectively, p,-q and q, -p.

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

Prove that the product of the perpendicular from the foci on any tangent to an ellipse is equal to the square of the semi-minor axis.

The two axes divide the plane into 4 parts called underline("") .

The locus of the point of intersection of two prependicular tangents of the ellipse x^(2)/9+y^(2)/4=1 is

Find the equation of the plane whose intercepts on the axes are 3,4,5 respectively.

Find the equation of an ellipse whose axes lie along the coordinate axes, which passes through the point (-3,1) and has eccentricity equal to sqrt(2//5)dot

Find the coordinates of the point on the curve sqrtx + sqrty = 4 at which tangent is equally inclined to the axes.

Find the equation of all possible curves such that length of intercept made by any tangent on x-axis is equal to the square of X-coordinate of the point of tangency. Given that the curve passes through (2,1)

The x-intercept of the tangent to a curve is equal to the ordinate of the point of contact. The equation of the curve through the point (1,1) is