Calendar: 1874-1875 Page 555

GENERAL LITERATURE AND SCIENCE 555 aar 2hxy by1 represents two straight lines and find the angle between them Prove that the equation bx2 2hxy ay2 represents two straight lines at right angles respectively to the two former 10 Prove that the equation of tbe circle of curvature of an ellipse at the point acosO 4sin is Xi a2 b2 cos30 sin30 3sin20 42 3cos20 11 Prove that if fixed conic be represented by the equation ax2 by2 2hxy 2gx 2fy the quantities 2icosa ab h2 -1- and sin-ω Sin2 ω where ω is the angle between the co-ordinate axes are indepen- dent of any special axes of reference 12 If α β γ be trilinear co-ordinates referred to triangle ABC interpret the equation Ιβγ mya ηαβ and if the curve represented be rectangular hyperbola prove that Zcos mcosB η co&C 13 Prove that the reciprocal of circle with respect to another circle is conic Find he lengths of the axes of the reciprocal in terms of the radii of the circles and the distance between their centres and show that two circles can always be reciprocated into pair of confocal conies 14 Find tbe equation to plane in the form xcosa cos ζ cosy And also the length of the perpendicular drawn from given point to it Determine the conditions that the planes