Conic Sections: Example 48

Topic

Quadratics

Description

This example illustrates a hyperbola, a type of conic section characterized by two separate curves called branches. The general equation of a hyperbola is ((x - h)²/a²) - ((y - k)²/b²) = 1 for horizontal hyperbolas or ((y - k)²/a²) - ((x - h)²/b²) = 1 for vertical hyperbolas. This example demonstrates how the hyperbola is positioned on the coordinate plane and how its equation reflects this position. Understanding hyperbolas is crucial for applications in physics and engineering, such as analyzing the paths of celestial bodies or designing certain types of antennas. Skills involved include identifying the hyperbola's center, axes, and asymptotes, and graphing it accurately.

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