Calendar: 1865-1866 Page 534

536 GENERAL LITERATURE AND SCIENCE 14 Find the values of χ which make mm maximum when β χ cos χ -f cos 2x -j- cos 32 a2 15 Given the base and vertical angle of triangle show that its area will he greatest when the remaining sides are equal 16 OA and OB are two groves meeting at so that OB 60 ball moves from towards another from Ο towards but twice as fast as the ball from find when the distance between the balls is the least possible and also this least distance II -Conic Sections Express the area of triangle in terms of the co-ordinates of its angular points Find the area of the triangle included between the lines 2y ha 2x- -y 7a χ Find the equation to the straight line which passes through the centres of the two circles χ and 4y Xs Show that two lines are represented by the equation Λ i2 and find them From point without circle two tangents OA OB are drawn and AB is chord From any straight line OPQR cutting the circle in the points Ρ and the chord in Prove that OP OQ OR are in harmonic progression chord QSQ' is drawn through the focus of parabola parallel to the tangent at any point Prove being the latus rectum SQ SQ' SP is the vertex is the centre the focus and Ρ any point in an ellipse Cd the conjugate diameter to the intersection of SΡ with CD Prove PQ AC If two chords of parabola intersect one another the rect-