| Vocab | Standard Equation | Find the Equation | Matching the Graphs | Miscellaneous |
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Asymptotes
Practice: Every hyperbola has two ______________ that intersect at the center of the hyperbola.
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(x-h)^2/a^2- (y-k)^2/b^2 = 1
and (y-k)^2/a^2- (x-h)^2/b^2 = 1
Practice: what is the standard equation of a hyperbola equation?
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(x-2)^2 / 4 - (y-2)^2 / 5 = 1
Practice: What is the equation for a hyperbola with the following equations?
Foci: (-1,2) and (5,2) vertices: (0,2) and (4,2) |
a. (x^2)/16-(y^2)/4=1
Practice: What is the correct equation for the following graph?
(See image 1) a. (x^2)/16-(y^2)/4=1 b. (y^2)/16-(x^2)/4=1 c. (y^2)/9-(x^2)/16=1 d. (y^2)/16-(x^2)/9=1 e. (y^2)/1-(x^2)/4=1 |
e=c/a
What is the equation for eccentricity of a hyperbola?
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Branches
Every hyperbola has two disconnected ______________.
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center: (0,0) vertices: (0, +/- 5) foci: (0, +/-13) asymptotes : y = +/-5/12x
Find the center, vertices, foci, and asymptotes of the hyperbola : x^2 - y^2 = 1
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(y^2 /4) - (x^2 /12) =1
What is the equation for a hyperbola with the following equations?
Vertices:(0,+/-2) Foci:(0,+/-4) |
b. (y^2)/16-(x^2)/4=1
What is the correct equation for the following graph?
(See image 2) a. (x^2)/16-(y^2)/4=1 b. (y^2)/16-(x^2)/4=1 c. (y^2)/9-(x^2)/16=1 d. (y^2)/16-(x^2)/9=1 e. (y^2)/1-(x^2)/4=1 |
Center: (1,-2)
Vertices: (3, -2) and (-1, -2) Foci: (1 ± √5, -2) Asymptotes: y= -2 ± (1/2)(x - 1)
Find the center, vertices, foci, and asymptotes for the following hyperbola: (x - 1)^2/4 - (y + 2)^2/1 =1
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A hyperbola is the set of all points (x,y) the difference of whose distances from two distinct fixed points is a positive constant.
What is a hyperbola?
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center: (0,0) vertices: (0,+/-5) foci: (0,+/-13) asymptotes: y= +/- 5/12x
y^2/25-x^2/144 = 1
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(17y^2/1024)- (17x^2/64)=1
What is the equation for a hyperbola with the following equations?
Foci:(0,+/-8) Asymptotes: y= +/- (3/4)x |
d. (y^2)/16-(x^2)/9=1
What is the correct equation for the following graph?
(See image 3) a. (x^2)/16-(y^2)/4=1 b. (y^2)/16-(x^2)/4=1 c. (y^2)/9-(x^2)/16=1 d. (y^2)/16-(x^2)/9=1 e. (y^2)/1-(x^2)/4=1 |
2x^2 - 3y^2 = 6 or x^2/3 - y^2/2 = 1
Find the equation of a hyperbola with a center at (0,0), vertices at (±√3, 0), and foci at ( ±√5, 0).
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The transverse axis is the line connecting the vertices and the center is the midpoint of the transverse axis.
What is the relationship between the transverse axis of a hyperbola and its center?
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center: (2,-6) vertices: (2,-5), (2, -7) foci: (2, -6+/-2^(1/3)) asymptotes: y= -6 +/-(x-2)
(y + 6)^2 - (x-2) ^2 = 1
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((x-4)^2 /4)- (y^2 /12) =1
What is the equation for a hyperbola with the following equations?
Vertices: (2,0) (6,0) Foci: (0,0) (8,0) |
c. (y^2)/9-(x^2)/16=1
What is the correct equation for the following graph?
(See image 4) a. (x^2)/16-(y^2)/4=1 b. (y^2)/16-(x^2)/4=1 c. (y^2)/9-(x^2)/16=1 d. (y^2)/16-(x^2)/9=1 e. (y^2)/1-(x^2)/4=1 |
Vertices: (0, ± 2)
Foci: (0, ± 4)
Find the vertices and foci of the hyperbola: y^2/4 - x^2/12 =1
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Horizontal Transverse Axis: The conjugate axis is the line segment of length 2b joining (h,k+b) and (h,k-b)
What is the conjugate axis of a hyperbola?
Vertical Transverse Axis: The conjugate axis is the line segment of length 2b joining (h+b,k) and (h-b,k) |
center: (2, -3) vertices: (3,-3), (1, -3) foci: (2 +/- 10^(1/2), -3) asymptotes: y = -3 +/- 3(x-2)
9x^2-y^2-36x-6y+18 = 0
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(y^2/9) - (4(x-2)^2 / 9) =1
What is the equation for a hyperbola with the following equations?
Vertices: (2,3) (2,-3) passes through (0,5) |
e. (y^2)/1-(x^2)/4=1
What is the correct equation for the following graph?
(See image 5) a. (x^2)/16-(y^2)/4=1 b. (y^2)/16-(x^2)/4=1 c. (y^2)/9-(x^2)/16=1 d. (y^2)/16-(x^2)/9=1 e. (y^2)/1-(x^2)/4=1 |
(x - 4)^2/4 - y^2/12 =1
Find the equation of a hyperbola with a vertices at (2, 0) and (6, 0), and foci at (0, 0) and (8, 0).
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