MATH 140 Lecture Notes - Lecture 38: Ellipse, Hyperbola
10 Dec 2015
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Math140 lecture 38 conic sections (cont. ) Let p 1 and p 2 be distinct points in the plane. Let | p 1 p 2 | > 2 a , where a is a positive. The points p such that make up a hyperbola. 0 = a2 + b2: for. Foci are at c, ), c b2 = 1 b x y2 a2 x2: vertices are at 0, a, asymptotes are y = b. Foci are at 0, c), c a x. Note: if a is fixed, c gets larger, so b gets larger b y = a x has a larger slope. Ex1: find the center, vertices, asymptotes, foci, and graph for y2 4. 9: axis of symmetry is the y-axis because x can never be zero. y2. 22 = 1: thus, vertices are at 0, 3, standard position, therefore the center is at (0, 0) o o, graph: are the asymptotes. are foci.
