More Practice with Hyperbolas

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Presentation transcript:

More Practice with Hyperbolas …in Sec. 8.3b

Nifty Practice Problems Write an equation for the given hyperbola. The hyperbola opens up-down: (2, –2) Plug in the point (2, –2): Equation:

Definition: Eccentricity of a Hyperbola The eccentricity of a hyperbola is where a is the semitransverse axis, b is the semiconjugate axis, and c is the distance from the center to either focus. Eccentricity of a hyperbola is always greater than 1!!!

Nifty Practice Problems Find an equation in standard form for the hyperbola with center at (0, 0), a = 4, e = 3/2, and a vertical focal axis. Start with a diagram? What’s the general equation? How about h and k? Now, how do we find a and b?

Nifty Practice Problems Find an equation in standard form for the hyperbola with center at (0, 0), a = 4, e = 3/2, and a vertical focal axis. The specific equation:

Nifty Practice Problems Find an equation in standard form for the hyperbola with center at (1, –4), c = 6, e = 2, and a horizontal focal axis.

Nifty Practice Problems Graph the given hyperbola, and find its vertices, foci, and eccentricity. Where’s the graph? Vertices: Foci: Eccentricity:

Nifty Practice Problems Graph the given hyperbola, and find its vertices, foci, and eccentricity.

Nifty Practice Problems Graph the given hyperbola, and find its vertices, foci, and eccentricity. Where’s the graph? Vertices: Foci: Eccentricity: