Writing the Equation of an Hyperbola Determine the center. Determine which way it opens (what variable comes first)? Determine the distance to the vertices (first denominator). Find the other denominator. (You may be given a focus or the equations of the asymptotes) Plug in all known values to write the equation. * Again… it can be helpful to sketch a quick graph!

Example 2 Write the equation of the hyperbola centered at the origin with a vertex at (4, 0) and Focus at (7, 0). Quick Sketch Opens Horizontally, so x comes first. Centered at origin so (h,k) = (0, 0) _____ __ _____ = 1 x2 y2 Also means… 42 33 Distance from center to vertex = 4 Distance from center to focus = 7 _____ __ _____ = 1 x2 y2 16 33 72 = 42 + b2 49 = 16 + b2 33 = b2

Example 3 Write the equation of the hyperbola centered at (2, 5) with a vertex at (2, 8) and asymptote y=(3/2)x + 2. Opens Vertically, so y comes first. Centered at (2, 5)=(h,k) 3 2 (y-5)2 (x-2)2 _______ __ _______ = 1 Also means… 32 22 Now draw box based on slope… Vertical distance = 3 (under y) Horizontal distance = 2 (under x) _______ __ _______ = 1 (y-5)2 (x-2)2 9 4

ASSIGNMENT Pg 449 23,24,25,27,28 Pg 453 16, 17, 18 Pg 475 35,3647