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 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.

P is the point on the parabola y^(2)=4ax(a>0) whose vertex is A .PA produced to meet the directrix in D and M is the foot of perpendicular from P on the directrix. If a circle is described on MD as a diameter, then its intersect x -axis at a point whose coordinates are