Table of Contents Hyperbola - Finding the Equation Horizontal AxisVertical Axis Recall that the equations for the hyperbola are given by...

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Presentation transcript:

Table of Contents Hyperbola - Finding the Equation Horizontal AxisVertical Axis Recall that the equations for the hyperbola are given by...

Table of Contents Slide 2 Hyperbola - Finding the Equation Summary of meanings of the constants: The vertices are a units from the center on the transverse axis. The center is at C(h, k). The foci are c units from the center on the transverse axis. The values of a, b, and c are related by the equation...

Table of Contents Slide 3 Hyperbola - Finding the Equation Example 1: Find the equation of the hyperbola with the given vertices and foci... The first step is to plot these points on a coordinate plane.

Table of Contents Slide 4 Hyperbola - Finding the Equation The center will be the midpoint of the line segment joining the vertices (also the foci)... The distance from the center to a vertex is a = 4. The distance from the center to a focus is c = 6.

Table of Contents Slide 5 Hyperbola - Finding the Equation Using the formula... the value of b can be found.

Table of Contents Slide 6 Hyperbola - Finding the Equation Summary: Since the vertices are vertical, the hyperbola has a vertical axis... and the equation is...

Table of Contents Slide 7 Hyperbola - Finding the Equation Example 2: Find the standard form of the hyperbola given by... Solution:

Table of Contents Slide 8 Hyperbola - Finding the Equation The standard form of the hyperbola is...

Table of Contents Hyperbola - Finding the Equation