Calendar: 1898-1899 Page 745

FACULTY OF SCIENCE cx111 YEARS II III may substitute any of the following for any of the preceding questions 16 If straight line intersect the sides BC CA AB of triangle in the points Dy respectively prove that BP CE AF DC' Ε FB If Χ Υ Ζ are the feet of the perpendiculars drawn from Ay to the opposite sides of the triangle and YZ9 ZXy XY meet BC7 CA AB respectively in prove that are collinear 17 In parabola prove that the foot of the perpendicular from the focus on any tangent lies on the tangent at the vertex and the perpendicular is mean proportional between the focal radius to the point of contact and half the semi- latus-rectum From any point Τ tangents are drawn to parabola inter- secting the directrix in Ρ and PL QL are drawn at right angles to TP TQ prove that are collinear 18 Prove that the normal chord of parabola that sub- tends right angle at the focus is divided by the axis in the ratio 19 Prove in any ellipse with the usual notation that PN2 AN Ν BC2 AC2 If AP meets the auxiliary circle in prove that the rectangle AP PR bears constant ratio to PN2 20 Prove that section of cone by plane parallel to generating line is parabola The sphere which contains the auxiliary circle and the centre of one focal sphere passes through the centre of the other focal sphere Cngonomctri IHfttretittal Calntlu£ Candidates for Special Matriculation Certificates may confine their attention to Questions 1-7 YEAR Define carefully the cosine of an angle and prove that if and Β are angles in two consecutive quadrants sin and