Conic Sections - Hyperbolas

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Presentation transcript:

Conic Sections - Hyperbolas

Hyperbola Hyperbola – is the set of points (P) in a plane such that the difference of the distances from P to two fixed points F1 and F2 is a given constant k. P F1 F2

Hyperbola Asymptotes Transverse Axis F1 F2 Vertices = (a, 0)

Hyperbola - Equation For a hyperbola with a horizontal transverse axis, the standard form of the equation is: P F1 F2

Hyperbola F1 Transverse Axis F2

Hyperbola - Equation For a hyperbola with a vertical transverse axis, the standard form of the equation is: F2 F1

Hyperbola Definitions: a – is the distance between the vertex and the center of the hyperbola b – is the distance between the tangent to the vertex and where it intersects the asymptotes c – is the distance between the foci and the center Relationships: The distances a, b and c form a right triangle and can be used to construct the hyperbola. Horizontal_Hyperbola.html Vertical_Hyperbola.html

Find the Foci Find the foci for a hyperbola: a2 b2 From the form, we know it’s a horizontal transverse axis. We know the foci are at (c, o ) and that c2 = a2 + b2 Foci are

Find the Foci Find the foci for a hyperbola: b2 a2 From the form, we know it’s a vertical transverse axis. We know the foci are at (0, c ) and that c2 = a2 + b2 Foci are

Write the Equation Write the equation of the hyperbola with foci at (5, 0) and vertices at (3, 0) c a From the info, it’s a horizontal transversal. We need to find b

Write the Equation Write the equation of the hyperbola with foci at (0, 13) and vertices at (0, 5) c b From the info, it’s a vertical transversal. We need to find a

Assignment