Applications of Trigonometric Functions Chapter 8 Applications of Trigonometric Functions

Section 4 The Hyperbola

A hyperbola is the set of all points P in the plane, the difference of whose distances from two fixed points, called the foci, is a constant. Pieces to a hyperbola: center, transverse axis, foci, vertices, and asymptotes Transverse Axis: is the line containing the center, vertices, and foci Vertices: share something in common with center and a = distance from center; U shapes are drawn using vertices Foci: two points on transverse axis, one inside each U shape, share a common piece with vertices and center and c = distance they are from center Asymptotes: lines drawn through the center; guide width of the U shapes

Important part of equations: x and y are both squared and subtracted from each, ORDER MATTERS transverse axis is determined by what comes first (a2 is always first) equation must always be equal to 1

Example: (#21 pg. 670) Foci: (-5, 0) and (5, 0); Vertex: (3, 0)

Example: (#45 pg. 670) Vertices: (-1, -1) & (3, -1); Asymptote: y + 1 = 3/2(x – 1)

Example: (#31 pg. 670) y2 – 9x2 = 9

Example: (#47 pg. 670) (𝑥−2) 2 4 − (𝑦+3) 2 9 =1

EXIT SLIP