10.4 Hyperbolas JMerrill 2010. Definition A hyperbola is the set of all points in a plane, the difference of whose distances from two distinct fixed point.

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Presentation transcript:

10.4 Hyperbolas JMerrill 2010

Definition A hyperbola is the set of all points in a plane, the difference of whose distances from two distinct fixed point (foci) is a positive constant.

Equations of Hyperbolas

Writing the Equation Find the equation of the hyperbola with vertices(-3, 2), (3, 2) and foci (-5, 2), (5, 2). Graph.

Find and Graph the Hyperbola State the direction of the transverse axis, sketch a graph and find the center, the vertices, and the foci. transverse axis: ◦v◦v ertical center: ◦(◦( -2, 1) vertices: ◦(◦( -2, 3), (-2, -1) foci:

Writing the Equation in Standard Form – You Try Given 4x 2 – 3y 2 + 8x + 16 = 0 You must complete the square

Eccentricity The same formula applies to both ellipses and hyperbolas. If the eccentricity is large, the branches of the hyperbola are nearly flat. If the eccentricity is close to 1, the branches are more narrow.