Calendar: 1870-1871 Page 513

general literature and science 513 If be drawn from one of the vertices perpendicular to tbe tangent at any point prove that tbe locus of the point of intersection of PS and QA produced will be circle Division -First Year III -analytical comctru anil Differential Calculus Explain the different methods of expressing algebraically the position of point of straight line What is meant by the equation to locust Interpret the fol- lowing equations χ θ xy α θ αθ Express in terms of their coordinates the distance between two given points and the angle the line joining them makes with the axis of Hence show that an equation of tbe first degree represents straight locus Find also the locus of point the sum of whose distances from two fixed points varies inversely as the difference Find the equation to straight line in terms of the length and direction of the perpendicular upon it from the origin Determine tbe factor such that Κ Ah Bk may be the distance of hk from tbe line Ax By the axes being oblique Prove that the radius of the circle inscribed in the triangle formed by the lines ρי η β 4- p2 si η β 4- ps si η γ Pv 23 -2 Α γ ρ a- sin 1-- sin -'- sin Find the equation to the straight line which passes through the origin and the point of intersection of the lines χ ך ϊ and show that it is perpendicular to the line when the axes are rectangular Κ Κ