Conic Sections: Overview of Hyperbola ( Click Hyperbola )

Definition: A hyperbola is a set of points equidistant from a single point. *

Equation: +/- x² /a² -/+ y² /b² = 1 Center= (0,0) (x-h)² /a²- (y-k)² /b²= r² Center = (h,k)

Important Concepts for Circles: Center, Foci Axis, Intercept(s)

Eccentricity (e = c/a & e>1) Distance: D=( (x-x)2 + (y-y)2)1/2 Midpoint: M = [(x+x)/2 , (y+y)/2)]

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Determine an equation for a Hyperbola: Center at (0,0) and Real Axis = 4 & Imaginary Axis =2:

- x^2/ 1^2 + y^2/ 2^2 = 1
- x^2/1^2 + y^2/2^2 = 1
- x^2+ y^2= 4

Determine an equation for a Hyperbola: Center at (-2, +3) and Major & Minor Axis =1:

(x-h)^2 / a^2- (y-k)^2 / b^2= r^2
(x+2)^2 / 1^2- (y-3)^2 /1^2= r^2
+x^2+ 4x +4 -y^2+ 6y -9 = 1
+x^2+ 4x -y^2+6y = +5

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Tom Love Malone College Fall 2007