Calendar: 1898-1899 Page 752

cxx faculty of science From the point cos cos י sin £ cos -י β tangents are drawn to the circle χ2 y2 a2 Find the coordinates of the points of contact in their simplest forms YEAR III may substitute any of the following for any of the previous Questions 21 The coordinates of are and of Β Find the equation of the locus of Ρ if the angle PAB is double of PBA 22 Find the equation of parabola of latus rectum 4a referred to Us vertex as origin and its axis as axis of Find where the straight line χ tan φ tan2 φ cuts the parabola and discuss your result giving the geo metrical significance of the angle φ 23 curve is defined by χ sec Θ tan θ prove that the chord joining the points for which θ α and θ β is cos β sin β cos β ct ο Hence obtain the equation of the tangent at h9 to x2 a2 y2 b2 24 Find the locus of the mid-points of system of parallel chords of the conic ax2 2hxy by2 2gx 2fy and hence find the condition that the lines mx mix should be parallel to pair of conjugate diameters of the conic algebra Candidates for Special Matriculation Certificates may confine their attention to Questions 1-8 YEAR Questions 1-11 YEAR II Questions 10-15 YEAR III Questions 13- 18 Prove that the difference between the two quotients that are obtained by dividing each of two numbers by the other is equal to the product of the two quotients that are obtained