Hyperbolas

The Hyperbola - Math

The standard equation for a hyperbola is: x2 a 2 y2 b = 1 with a>b>0 Once that is given to us, we de ne a focus and directrix: c= p a2 + b2 F=(c;0) e= c a >1 L= fx= a e g and the new quantity eis called the eccentricity of the hyperbola Remark on Eccentricity: The eccentricity is the value eso that: jPFj= ejPLj is the equation of the conic

Equations of Hyperbolas

Points on the hyperbola are 24 units closer to one focus than the other (y − 10) 2 144 − (x + 10) 2 16 = 1 22) Center at (−1, −1) Transverse axis is vertical and 24 units long Congujate axis is 8 units long (y + 1) 144 − (x + 1) 16 = 1-2-Create your own worksheets like this one with Infinite Algebra 2 Free trial available at

Hyperbola - Sakshi Education

HYPERBOLA Equation of a Hyperbola in Standard From The equation of a hyperbola in the standard form is 2 2 2 2 x y 1 a b − = Proof: Let S be the focus, e be the eccentricity and L = 0 be the directrix of the hyperbola Let P be a point on the hyperbola Let M, Z be the projections of P, S on the directrix L = 0 respectively

Writing Equations of Hyperbolas Date Period

Points on the hyperbola are units closer to one focus than the other 22) Center at ( , ) Transverse axis is vertical and units long Conjugate axis is units long 23) Center at ( , ) Transverse axis is vertical; central rectangle is units wide and units tall

Hyperbolas

the hyperbola at two points, called the vertices The segment connecting the vertices is called the transverse axis of the hyperbola The center of the hyperbola is located at the midpoint of the transverse axis As x and y get larger the branches of the hyperbola approach a pair of intersecting lines called the asymptotes of the hyperbola

28 Conic Sections: Hyperbolas

• Define a hyperbola in a plane • Determine whether an equation represents a hyperbola or some other conic section • Graph a hyperbola from a given equation • Determine the center, vertices, foci and eccentricity of a hyperbola • Find the equation of a hyperbola from a graph or from stated properties

Hyperbolas

1 Determine the equation of a hyperbola with vertices (2,-3) and (8,-3) and focus at (0,-3) 2 Determine the equation of a hyperbola with vertices (2,4) and (2,-6) and equation of an asymptote 12 2 3 yx Restart when you are ready to check your answers

7-3 Hyperbolas

model the hyperbola Write an equation for the hyperbola with the given characteristics The center is at (5, 1), a vertex is at (5, 9), and an equation of an asymptote is 3 y = 4 x ± 17 62/87,21 The center is located at (5, 1), so h = 5 and k = 1 One vertex is located at (5, 9), so a = 8 and a2 = 64 Because the

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