Calendar: 1877-1878 Page 598

596 GENERAL LITERATURE AND SCIENCE 13 If two equal tangents to parabola be cut by third tangent their alternate segments are equal 14 If from an external point Ο pair of tangents OQ OQf be drawn to parabola and the chord QQ' be joined the area of the figure bounded by QCjf and the curve is two-thirds of the triangle 15 Trace the curve χ xz and determine whether the straight line χ is tangent to it 16 Two straight lines are drawn from the vertex of parabola at right angles to each other the points where these straight Hues meet the curve are joined thus forming right-angled triangle find the least area of tiiis triangle 17 If PC be the semi-minor axis of an ellipse then BC CA CS2 and if SL be the latus rectum SL AC BC Also if SBS' be right angle then CA2 2CB2 18 The tangent to the ellipse at any point Ρ makes equal angles with the focal distances SP and S'P In an ellipse the tangent at any point makes greater angle with the focal distance than with the perpendicular on tbe directrix 19 If PAT be the ordinate of any point Ρ on the ellipse then PN2 AN A'Ν BC2 AC If to point on the ellipse AQ A'Q be drawn meeting NP in and then NB NS NP2 20 If from the foci and S' SY and S'Y' are drawn at right angles to the tangent at then י and Γ' are on the cireum- ference of the auxiliary circle and SY S'Y BC2 21 Tbe area of the ellipse is to tbe area of the auxiliary circle as ΒC to AC 22 For what position of Ρ on the ellipse 13 the angle SPS' greatest 23 If series of ellipses be described having the same major axis tbe tangents at the ends of their latera recta will pass through one or other of two fixed points 24 Find the equation to the ellipse referred to axes passing through the ends of the minor axis and meeting at one end of the major axis