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Hyperbola

Hyperbola. Definition : A hyperbola is a set of points in the plane such that the difference of the distances from two fixed points, called foci, is constant. (A hyperbola consist of 2 branches and asymptotes). Vocabulary. Foci: Two fixed points on the transverse axis

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Hyperbola

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  1. Hyperbola • Definition: A hyperbola is a set of points in the plane such that the difference of the distances from two fixed points, called foci, is constant. (A hyperbola consist of 2 branches and asymptotes)

  2. Vocabulary • Foci: Two fixed points on the transverse axis • vertices: Point of intersection of the hyperbola and the transverse axis • Transverse axis: The transverse axis is the line segment joining the vertices(passes through the foci) • Conjugate axis: The line perpendicular to the transverse axis • Center: midpoint of the transverse axis • Asymptote: Lines the hyperbola approach but do not cross A hyperbola can have either a horizontal or vertical transverse axis.

  3. Hyperbola with horizontal transverse axis (x-term positive) • Equation (center: ( h, k)) a-distance from center to vertex b- distance from center to endpoint of conjugate axis. c: distance from center to focus. Asymptote: y= b x , y= -b x a a

  4. Hyperbola with vertical transverse axis (y-term positive) Equation ( center : h,k)

  5. Graphing a hyperbola • Put the equation in standard form, if necessary • Determine whether the graph opens left and right or up and down. (Which term is positive? ) 3. Plot the center point, (h, k). 4. Find and plot the vertices.

  6. 5. Draw vertical and horizontal lines, forming a rectangle 6. Draw the asymptotes. They will pass through the origin and the corners of the rectangle. 7. Draw the hyperbola. Remember it gets infinitely close to the asymptotes but never touches or crosses them.

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