MATH 140 Lecture 38: Hyperbolas and the General Form
9 Dec 2015
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Math140 lecture 38 conic sections (cont. ) Let p1 and p2 be distinct points in the plane. Let |p1 p2| > 2a, where a is a positive constant. The points p such that ||p1 p| |p2 p||=2a make up a hyperbola. Foci are at a2 x2 (0, a) Foci are at ( c,0) ,c= a2+b2 (0, c) ,c= a2+b2 b2 =1 : y2: for x x. Note: if a is fixed, c gets larger, so b gets larger y= b a x has a larger slope. Ex1: find the center, vertices, asymptotes, foci, and graph for. 9: axis of symmetry is the y-axis because x can never be zero, re-write formula: y2. 22 =1 a=3,b=2 (0, 3: thus, vertices are at, standard position, therefore the center is at (0, 0) y= 3. 2 o x are the asymptotes. c= 9+4= 13 (0, 13) o: graph: are foci.
