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 point P (5, 3) was reflected in the origin to get the image P'. If N is the foot of the perpendicular from P' to the x-axis, find the co-ordinates of N.

If P and Q a be a pair of conjugate points with respect to a circle S . Prove that the circle on PQ as diameter cuts the circle S orthogonally.

The coordinates of the foot of perpendicular drawn from the point P(-2,5,4) on the x-axis are

L is the foot of perpendicular drawn from a point P(3,4,5) on x-axis. The coordinates of L are

The tangent at point P on the ellipse x^(2)/a^(2) + y^(2)/b^(2) = 1 cuts the minor axis in Q and PR is drawn perpendicular to the minor axis. If C is the centre of the ellipse, then CQ*CR =

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

Let the tangent at a point P on the ellipse meet the major axis at B and the ordinate from it meet the major axis at A. If Q is a point on the AP such that AQ=AB , prove that the locus of Q is a hyperbola. Find the asymptotes of this hyperbola.

Shwo that the difference of the squares of the tangents to two coplanar circles from any point P in the plane of the circles varies as the perpendicular from P on their radical axis. Also, prove that the locus of a point such that the difference of the squares of the tangents from it to two given circles is constant is a line parallel to their radical axis.

P is a point on the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 , and N is the foot of the perpendicular from P on the transverse axis. The tantent to the hyperbola at P meets the transverse axis at T. If O is the centre of the hyperbola, then OT.ON is equal to