# Calendar: 1863-1864 Page 527

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GENERAL LITERATURE AND SCIENCE 527 Find the point of intersection of the lines sec and sec and the angle "between them If Ρ be line drawn parallel to Β the base of the triangle ABC find the locus of the intersection of Β Ρ and CQ Change the co-ordinates of point to other co-ordinates the axes both rectangular being inclined at given angle the origin remaining the same Example yf the angle 45 Find the equation to the circle passing through three points the co-ordinates of which are The equation to the lines bisecting the angles between the lines represented by the equation Ax Bxy -I- Cf is Β y2 2xy If in an ellipse MP be produced to meet the circle on the axis major in and SP CQ be joined find the locus of their in- tersection Find the equation to the tangent of parabola Express it in the form mx A- Two tangents to parabola include constant angle Find the locus of their intersection 10 CP and CD are two semi-conjugates to an ellipse Given the co-ordinates of find those of and thence prove that CP2 CD2 CA2 CB2 11 rod AB slides between two oblique axes and Β are perpendicular to them Find the equation to the curve which is the locus of 12 If ρ and p1 be the perpendiculars from the foci and Η on the tangent to an ellipse show that ρ ρ 13 If one root of x3 15 χ he V2 fi"d all the roots 14 If be the roots of xs qx -f- form the equation whose roots shall be

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