Calendar: 1869-1870 Page 512

514 GENERAL LITERATURE AND SCIENCE If represent one of these lines 3ןן another and ry third find the area included by them Show that the lines represented by vtf 2x cut at 45 Find the polar coordinates of the two points V3 and the distance between them Straight lines cut off intercepts from the axes the sum of their reciprocals being constant show that all such lines pass through fixed point Show without using rectangular coordinates that the equa- tion Λ cos Θ Br sin is straight line Draw tangent to the circle -j- y1 ax -f by and show that the tangent at the origin cuts the axis of at an angle -U In the ellipse prove that Ρ CD CB CA In the ellipse find the eccentric coordinates of Ρ and and use them to find the locus of the bisection of the chord PQ 10 If the line SP he inclined at an angle θ to the axis of the coordinates of being then the distance of Ρ from the origin A2 £s 42 cos θ sin Θ 11 Find the equation to the chord of contact in the parabola the common point of tangents being Ak and show that the area of the triangle formed by the two tangents and their chord A1 4ah 2ev 12 Two Hnes CA CB are cut by line OAB point Ρ is taken in AB tbat OA OP and OB are in harmonic pro- gression show that the locus of Ρ is straight line passing through XII -Contr Stittonif II What value must be given to that eJ3 χ may represent two right lines