MA 22S1
Assignment 3
Due 2-4 November 2015
Id:
22S1-f2015-3.m4,v 1.1 2015/10/26 15:30:43 john Exp john
1. For each of the following, determine whether it is an ellipse, parabola,
hyperbola or degenerate. In the degenerate case you don’t need to
specify which kind of degenerate conic it is.
(a) x2 + 2xy + 3y 2 + 4x + 5y + 6 = 0
(b) x2 + 2xy + 3y 2 + 4x + 5y − 6 = 0
(c) 3x2 − 4xy − 4y 2 + 10x + 4y − 3 = 0
(d) 3x2 − 4xy − 4y 2 + 10x + 4y + 3 = 0
(e) x2 − 4xy + 4y 2 + 6x − 12y + 4 = 0
(f) x2 − 4xy + 4y 2 + 3x − 14y + 8 = 0
2. The set of (x, y) where
94x2 − 360xy − 263y 2 + 572x + 494y − 338 = 0
is a hyperbola.
(a) Put it in standard form via an appropriate change of variables.
1
Id:
22S1-f2015-3.m4,v 1.1 2015/10/26 15:30:43 john Exp john 2
(b) Find its eccentricity.
(c) Find its asymptotes in the original coordinate system.