# Calendar: 1896-1897 Page 695

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FACULTY OF SCIENCE CV Scribing cylinder of which the axis is perpendicular to tlie planes square side 20 inches circumscribes sphere of 10 inches radius through the middle points of each pair of ad- jacent sides planes are drawn at right angles to the plane of the square cutting off segments of the sphere Find within 1q of square inch the area of the remaining surface of the phere algebraic eomctn YEARS II III 13 Find the distance between two points of which the coordinates with respect to pair of rectangular axes are given Prove algebraically that the sum of the squares on two sides of triangle is double of the sum of the squares on half the third side and on the median bisecting the third side 14 Arrange the equation of the straight line 12x 5y l3 so as to shew the intercepts it cuts off from the axes ii its inclination to the axis of Find the equation of straight line perpendicular to 2x 3y cutting off intercepts from the axes the sum of which is the same as the sum of those of the given straight line 15 Prove that x2 y2 bxy represents pair of straight lines at right angles to one another and find the angle between the pair of straight lines represented by y2 2Vary x2 16 Find the coordinates of the centre the length of the radius and the equations of the tangents at the points of intersection with the axes of the circle x2 y2 6x 8y YEAR III may substitute any of the following for Questions 9-16 17 What is the eccentric angle of point onan ellipse If the normal at point of which the eccentric angle is meets the ellipse again at point of which the eccentric angle is 3y prove that tan γ χ χ

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