Calendar: 1881-1882 Page 632

GENERAL LITERATURE AND SCIENCE 633 parabola on the asymptotes of the former is the same for all members of the system 10 Trace the followmg curves 2x4 ccy -f bx Ay 6y x-4y lyh 6xy 11 Show that the equation to the circumscribing circle in areal co-ordinates is L2 £2 Hence determine the condition that the general equation of the second degree Ax By2 4- Cz 42 Dy2 2Ezx 42 Fyx represents circle Find the equation to the circle which passes through two angular points and the centre of gravity of the fundamental triangle 12 Determine the nature of the following curves xy r2 42y ly1 10 r2 Find the centre and asymptotes of the hyperbola z1 ψ χ 2y2 42 xz Sxy 13 If the equation to conic by given by xy ax2 42 bxy of 2dx 2ey show that the eccentricity is given by 62 4- cf e2 י also that the line or Λ 4- e2 is parallel to the directrices 14 Show that the equation to the two tangents drawn from x'y' to the conic xy is xy x'y Fi xy where xy is the equation to the polar of x'y' Hence prove that the equation to the director-circle or locus of tangents at right angles is b2-ac τ2 4- 42 be cd 2y d'0-ae d2 e2 '0