Section 10 4 Conic Sections Hyperbolas Hyperbola is

Section 10. 4 Conic Sections Hyperbolas

Hyperbola – is the set of points (P) in a plane such that the difference of the distances from P to two fixed points F 1 and F 2 is a given constant k. P F 1 F 2

Hyperbola Asymptotes Transverse Axis F 1 F 2 Vertices = ( a, 0)

Hyperbola - Equation For a hyperbola with a horizontal transverse axis, the standard form of the equation is: P F 1 F 2

Hyperbola F 1 F 2 Transverse Axis

Hyperbola - Equation For a hyperbola with a vertical transverse axis, the standard form of the equation is: F 2 F 1

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: a 2 b 2 From the form, we know it’s a horizontal transverse axis. We know the foci are at ( c, o ) and that c 2 = a 2 + b 2 Foci are

Find the Foci Find the foci for a hyperbola: b 2 a 2 From the form, we know it’s a vertical transverse axis. We know the foci are at (0, c ) and that c 2 = a 2 + b 2 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

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