O is the centre of an ellipse whose semi-minor axis is b . The ordinate of a point P of the ellipse intersects its auxiliary circle at Q (when produced). The straight line through P drawn parallel to OQ cuts the major axis at G . Prove that , PG = b .

Two circles intersect each other at the points G and H . A straight line is drawn through the point G which intersect two circles at the points P and Q and the straight line through the point H parallel to PQ intersects the two circles at the points R and S . Prove that PQ=RS .

The diagonals AC and BD of the parallelogram ABCD intersect each other at O . Any straight line passing through O intesects the sides AB and CD at the points P and Q respectively . Prove that OP = OQ.

Show that the tangent at any point on an ellipse and the tangent at the corresponding point on its auxiliary circle intersect on the major axis.

Two circles intersect each other at the points P and Q. Two straight lines through P and Q intersect on circle at the points A and C and the other circle at B and D . Prove that AC||BD.

Two circles intersect each other at the points P and Q. A straight line passing through P intersects one circle at A the other circle at .A straight line passing through Q intersect the first circle at C and the second circle at D. Prove that AC||BD .

The center of an ellipse is C and P N is any ordinate. Point A ,A ' are the endpoints of the major axis. Then find the value of (P N^2)/((A N)dotA'Ndot)

The straight line PAB intersects the circle with centre O at the points A and B. The straight line PAB will be a tangent to that circle if AB ="_______"

Two parallel straight lines are drawn through the points of intersection of two circles upto their circumference. Then prove that two straight lines are equal.

P is the point on the ellipse is x^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.

(b) Find the equation of the straight line parallel to the y-axis and passing through the point (-1,-7) .