The tangent at a point `P` on an ellipse intersects the major axis at `T ,a n dN` is the foot of the perpendicular from `P` to the same axis. Show that the circle drawn on `N T` as diameter intersects the auxiliary circle orthogonally.

The tangent at a point P on an ellipse intersects the major axis at T, and N is the foot of the perpendicular from P to the same axis.Show that the circle drawn on NT as diameter intersects the auxiliary circle orthogonally.

The circle on SS' as diameter intersects the ellipse in real points then

Show that the tangents at the ends of a latus rectum of ellipse intersect on the major axis.

Q is a point on the auxiliary circle of an ellipse. P is the corresponding point on ellipse. N is the foot of perpendicular from focus S, to the tangent of auxiliary circle at Q. Then

IfN is the foot of the pcrpendicular drawn from any point P on the ellipse z (a b) to PV its major axis AA then AN A N

The length of the foot of perpendicular drawn from the point P(3, 6, 7) on y-axis is

If the perpendicular distance of a point P from the X-axis is 5 units and the foot of the perpendicular lies on the negative direction of X-axis then the point P has

Consider an ellipse x^2/25+y^2/9=1 with centre c and a point P on it with eccentric angle pi/4. Nomal drawn at P intersects the major and minor axes in A and B respectively. N_1 and N_2 are the feet of the perpendiculars from the foci S_1 and S_2 respectively on the tangent at P and N is the foot of the perpendicular from the centre of the ellipse on the normal at P. Tangent at P intersects the axis of x at T.