Calendar: 1880-1881 Page 633

GENERAL LITERATURE AND SCIENCE 633 The ordinate to the diameter through any point on parabola is mean proportional between the corresponding abscissa and four times the focal distance of the point If through fixed point straight line is drawn meeting two fixed lines OD OE in respectively and on it point Ρ is taken such that CAP AB2 prove that the focus of Ρ is parabola which passes through and Ο and has its axis parallel to OD and the tangent at parallel to OE The two tangents drawn to an ellipse from an external point subtend equal angles at either focus At the extremi- ties of focal chord of an ellipse tangents and normals are drawn prove that the line joining the intersections passes through the other focus Find the distance of the point lc from the line χ cos sin ρ Find the equation to the line perpendicular to mx 40 through the intersection of the straight lines mx £ Find the cosine of the angle between the lines Ix my Vx m'y Find the equation of straight line referred to polar chords Given the angles of triangle one vertex is fixed another moves along straight line find the locus of the third vertex Find the radius of the circle a2 f2 ra 2by Prove that the circle which passes through any three of the four points where the rectangular hyperbola 12 2מ hxy y2 2yx 2fy cuts the axes is equal to the circle x2 V2 2fy Find the equation of tangent to parabola and show that that of normal is am3