Calendar: 1899-1900 Page 771

faculty of science cxix 10 Integrate the equation χ n2& by graphical construction and show how the solution may be adapted to any given initial circumstances of velocity and position 11 Explain the statement of the Second Law of Motion in the form mv dt uniform chain lies on table and one end is seized and acted upon by constant force equal to two-thirds of the weight of the chain shew that the chain will be just lifted off the table IV nalgttcal eieometrg Find the area of triangle in terms of the coordinates of its vertices Verify that the lines joining the vertices of triangle to the middle points of the opposite sides divide the triangle into six parts of equal area Two sides of parallelogram are the lines 2x by 4x 3y and the opposite pair intersect in the point Find the area of the parallelogram Show that the equation x2 y2 2xy cos ω 2gx 2fy epresents circle and find the length of the tangent to it from any point Prove analytically that there are two circles which pass through two given points and touch given straight line and shew them in figure Prove that the family of straight lines χ ty at2 where has any value all touch parabola If line intersect two given lines OJ Ο'Ά in points Ρ P' so that OP O'P the line touches parabola