# Calendar: 1867-1868 Page 485

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486 GENERAL LITERATURE AND SCIENCE 15 Sum the series to infinity- 8in sin sin 2a tin sin 3a -f- 2' ο sin3 sin &c and prove De Moivre's formula in every case 16 If AO BO CO be three lines bisecting the angles of the triangle ABC show that AO BO CO tan Λ tan tan AB BC AC Division III IF III -Conic Sections The equation xy represents two straight lines inclined at an angle tan-3 Find the equation to straight line which is perpendicular to 5x 3y and which cuts the axis of at distance 10 from the origin Find the relation between and that the line may touch the circle x11 c2 Find the equation to the parabola the axes being diameter and the tangent at the point where it meets the curve Deduce the polar equation to the ellipse round the focus from the rectangular equation round the centre Three tangents to parabola which have the tangents of their inclinations in harmonica progression will form triangle of constant area The chords of circle concentric with the ellipse 3L -j- are tangents to the ellipse show that the locus of A8 the middle points of the chords is defined by x2 y2 4y In the ellipse show that PQ the normal l- JSP-HP' Find the locus of the bisection of PG

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