Calendar: 1864-1865 Page 542

544 GENERAL LITERATURE AND SCIENCE Trace the curve x2 a2 a4 and draw its asymptotes What will be the alteration in the form of the curve if the equation be 0s Xs a4 10 If APB one of series of straight lines cut off from the axes two lines OA and OB such that OA OB find the locus of their intersections 11 Define multiple point and conjugate point Show that if xy be the equation to the curve which has either of this class of points that is indeterminate when ax dx dy dx 12 Find the species of point at the origin of the curve of which the equation isy4 -f- 2axy3 as 13 Find the radius of curvature and the co-ordinates of the evolute of the curve defined by the equation -I 2y ec 14 Find the values of and which make b" maximum when χ constant quantity 15 Find the area of spherical triangle in terms of its angles 16 If Ε be the spherical excess in right-angled triangle where show that tan tan tan II -iHtjrrtJ ilHatijcmattcs Define similar figures prove Lemma and show that cycloids are similar figures If body revolve in an ellipse round the centre find the law of force railway engine travels at the rate of 24 miles an hour