Q is the point on the auxiliary circle corresponding to P on the ellipse; PLM is drawn parallel to CQ to meet the axes in `L and M` prove that `PL = b and PN = a`.

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

Q is a point on the auxiliary circle corresponding to the point P of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1. If T is the foot of the perpendicular dropped from the focus s onto the tangent to the auxiliary circle at Q then the Delta SPT is

P & Q are the corresponding points on a standard ellipse & its auxiliary circle. The tangent at P to the ellipse meets the major axis in T. Prove that QT touches the auxiliary circle.

P is the point on the ellipse isx^2/16+y^2/9=1 and Q is the corresponding point on the auxiliary circle of the ellipse. If the line joining the center C to Q meets the normal at P with respect to the given ellipse at K, then find the value of CK.

P and Q are corresponding points on the ellipse x^(2)/a^(2) + y^(2)/b^(2) = 1 and the auxiliary circle respectively . The normal at P to the elliopse meets CQ at R. where C is the centre of the ellipse Prove that CR = a +b

The tangent at any point to the circle x^(2)+y^(2)=r^(2) meets the coordinate axes at A and B.If the lines drawn parallel to axes through A and B meet at P then locus of P is

Any point X inside D E F is joined to its vertices. From a point P in D X ,\ P Q is drawn parallel to D E meeting X E at Q and Q R is drawn parallel to E F meeting X F in R . Prove that P R D F .

Two equal circles intersect in P and Q.A straight line through P meets the circles in A and B. Prove that QA=QB

Ois the origin & also the centre of two concentric circles having radii of the inner & the outer circle as a & b respectively. A line OPQ is drawn to cut the inner circle in P & the outer circle in Q. PR is drawn parallel to the y-axis & QR is drawn parallel to the x-axis. Prove that the locus of R is an ellipse touching the two circles. If the focii of this ellipse lie on the inner circle, find the ratio of inner: outer radii & find also the eccentricity of the ellipse.