Calendar: 1881-1882 Page 630

GENERAL LITERATURE AND SCIENCE 631 XTV Seometri If from any point without circle two straight lines be Irawn one of which cuts the circle and the other touches it the rectangle contained by the whole line which cuts the circle and the part of it without the circle shall be equal to the square on the line which touches it If from point two tangents OA OB and chord OPQ be drawn to ircle and AP AQ produced meet OB in Ε and then shall BF BE2 Ε E0 FA F0 If straight line cut the sides of triangle ABC in DEF then will BD CE AF DO EA FB quadrilateral is formed by four straight liiies AB BCy CD DA fifth straight line meets these in the points respectively Prove the corresponding property namely- AE BF CG DH AH BE CF DG Prove that tangents to parabola at the extremities of focal chord intersect at right angles on the directrix Two equal parabolas have common vertex but axes inclined at an angle of 60 Show that their directrices inter- sect in point bisecting the line joining the intersections of the tangents at the extremities of the common focal chord The product of the perpendiculars from the foci of an ellipse on the tangent at any point is constant and equal to the square on the semi-minor axis circle is described on the perpendicular CY let fall from the centre on the tangent to an ellipse as diameter This circle meets the circle described on the minor axis as diameter in Show that the difference of the focal perpendiculars 2YQ State how the position of point is determined in Analytical Geometry By Cartesian co-ordinates By Areal co-ordinates