Calendar: 1861-1862 Page 495

496 GENERAL LITERATURE AND SCIENCE Find the area of the triangle formed by the intersection of 2x 3x From any external point two tangents may be drawn to circle Show that hy hxf Cנ kf represents two tangents to the circle x2 y2 c2 which pass through and Find the equation to parabola the axes being the diameter and the tangent at the point where it meets the curve 10 Given the position of the focus of parabola which touches given right line find the locus of the vertex 11 Find the equation to the tangent of an ellipse Find the locus of the intersection of the tangent with the perpendicular on it from the centre 12 If the chord and diameter of an ellipse are parallel the supplemental chord is parallel to the conjugate diameter 13 Find the equation to the hyperbola when the asymptotes are axes 14 Find the locus of the middle points of the focal chords of an ellipse II -fHteallanrouS anB Cljrorn of equations When two curves intersect find the angle of intersection and find the co-ordinates of the point and the angle when the curves are defined by 2ax andy3 axy -J- a3 Integrate- tj dx And show thatf-"1 dx sin mx Vi ן of χ and χ infinity If sec then ks x' If through given point Ρ straight line Β is drawn