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Standard Form of Hyperbolas: Characteristics, Equations, and Graphing Techniques

This lesson explores hyperbolas in standard form, focusing on their key characteristics, including the major axis and asymptotes. The session covers deriving the equation of a hyperbola from given foci and asymptote information, with examples illustrating how to sketch hyperbolas, find coordinates of vertices and foci, and determine eccentricity. Additionally, comparisons with ellipses highlight differences in their properties. Homework exercises reinforce the concepts, allowing students to practice finding key features and equations related to hyperbolas.

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Standard Form of Hyperbolas: Characteristics, Equations, and Graphing Techniques

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  1. 9.5 Hyperbolas (Day 2)

  2. (FROM YESTERDAY) Standard Form of Hyperbolas Major axis is on the x-axis: Major axis is on the y-axis: asymptotes a2 is on (+) variable Vertices & Foci on x-axis Vertices & Foci on y-axis “C A B” Foci:

  3. Ex 1) Write an equation of a hyperbola with asymptotes and foci Make a sketch of asymptotes Rise = 3 Run = 4 Foci on x- axis → x2 is (+) variable a is on x- axis & b is on y- axis on x- axis on y- axis

  4. Ex 2) Find an equation of a hyperbola having foci (-3, 0) and (3, 0) and difference of focal radii equal to 4 Diff. of focal radii = 2a Foci are ± c on x- axis (Same as Sum for Ellipse) on x- axis foci on same axis as ‘a’

  5. Compare Ellipse & Hyperbola Ellipse a2 is larger # Hyperbola a2 is with (+) variable “C A B” Foci (‘c’) on same axis as ‘a’ Eccentricity = BOTH

  6. Homework #909 Pg. 430 2, 4, 6, & 13 – 18 all Pg. 421 1, 3, 5 When graphing, find: x-intercepts y-intercepts coordinates of foci eccentricity length of major axis (if ellipse) equations of asymptotes (if hyperbola)

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