Calendar: 1859-1860 Page 442

GENERAL LITERATURE AND SCIENCE 443 MATHEMATICS -MIDDLE SCHOLARSHIP tonutrg of ttoo tmtnfitonS Find the equation to straight line in terms of the perpen- dicular from the origin on it Ex it '2 S3 find ρ and Find the tangent of the angle between two straight lines referred to oblique axes Ex mx my χ also when Find the area of the triangle formed by the straight lines 2x 3x and χ Find the equation to the tangent of the circle Ex y2 x2 16 when χ In the parabola show that ST SP SG Find the equation to the parabola the axes being any diameter and the tangent at the point where it meets the curve If Ρ normal to point Ρ in parabola be produced to meet the curve in find length of PQ Find the equation to an ellipse and from it deduce the polar equation the centre being the pole Find the equation to the tangent in terms of its inclination to the axis of χ and if 2x2- -3y2 find the point such that the tangent is equally inclined to both axes 10 Prove that CT CN CA2 ST HZ BC2 11 Define conjugate diameters given the co-ordinates of the extremity of one diameter find those of the extremity of the conjugate 12 The area of the parallelogram described at the end of conjugate diameters is constant 13 Define an asymptote find the equation to the hyperbola referred to the asymptotes as axes