9.5A Graph Hyperbolas Algebra II.

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Presentation transcript:

9.5A Graph Hyperbolas Algebra II

Hyperbolas Like an ellipse but instead of the sum of distances it is the difference A hyperbola is the set of all points P such that the differences from P to two fixed points, called foci, is constant The line thru the foci intersects the hyperbola @ two points (the vertices) The line segment joining the vertices is the transverse axis, and it’s midpoint is the center of the hyperbola. Has 2 branches and 2 asymptotes The asymptotes contain the diagonals of a rectangle centered at the hyperbolas center

(0,b) (0,-b) Asymptotes Vertex (a,0) Vertex (-a,0) Focus Focus This is an example of a horizontal transverse axis

Vertical transverse axis

Standard Form of Hyperbola w/ center @ origin Equation Transverse Axis Asymptotes Vertices Horizontal y=+/- (b/a)x (+/-a,o) Vertical y=+/- (a/b)x (0,+/-a) Foci lie on transverse axis, c units from the center c2 = a2+b2

Ex. 1)Graph Write in standard form (divide through by 144) a=4 b=3 transverse axis is vertical & vertices are (0,4) & (0, -4) Plot other pts from b value (3,0) , (-3,0) to make rectangle Draw a rectangle centered at the origin. Draw asymptotes. Draw hyperbola with foci.

Graph

Ex. 2 Graph

9.5B Write Equations of Hyperbolas Algebra II

Ex. 1)Write the equation of a hyperbola with foci (0,-3) & (0,3) and vertices (0,-2) & (0,2). Vertical because foci & vertices lie on the y-axis Center @ origin because f & v are equidistant from the origin Since c=3 & a=2, c2 = b2 + a2 9 = b2 + 4 5 = b2 +/-√5 = b

Standard Form of Hyperbola w/ center @ origin Equation Transverse Axis Asymptotes Vertices Horizontal y=+/- (b/a)x (+/-a,o) Vertical y=+/- (a/b)x (0,+/-a) Foci lie on transverse axis, c units from the center c2 = a2+b2

Ex. 2 Write an equation of the hyperbola with the given foci & vertices #25

Assignment