What is the standard equation of a hyperbola with center at the origin and transverse axis along the x-axis?
A
x²/a² - y²/b² = 1
B
y²/a² - x²/b² = 1
C
x²/a² + y²/b² = 1
D
y²/a² + x²/b² = 1
Analysis & Theory
For transverse axis along x-axis, the equation is x²/a² - y²/b² = 1.
What is the standard equation of a hyperbola with center at the origin and transverse axis along the y-axis?
A
x²/a² - y²/b² = 1
B
y²/a² - x²/b² = 1
C
x²/a² + y²/b² = 1
D
y²/b² - x²/a² = 1
Analysis & Theory
For transverse axis along y-axis, the equation is y²/a² - x²/b² = 1.
In the hyperbola x²/a² - y²/b² = 1, what are the coordinates of the foci?
A
(±c, 0)
B
(0, ±c)
C
(±a, 0)
D
(0, ±b)
Analysis & Theory
For hyperbola with transverse axis along x-axis, foci are at (±c, 0) where c² = a² + b².
In the hyperbola y²/a² - x²/b² = 1, what are the coordinates of the foci?
A
(±c, 0)
B
(0, ±c)
C
(±a, 0)
D
(0, ±b)
Analysis & Theory
For hyperbola with transverse axis along y-axis, foci are at (0, ±c) where c² = a² + b².
In the hyperbola x²/a² - y²/b² = 1, what are the equations of the asymptotes?
A
y = ±(b/a)x
B
y = ±(a/b)x
C
y = ±a
D
x = ±b
Analysis & Theory
For x²/a² - y²/b² = 1, asymptotes are y = ±(b/a)x.
In the hyperbola y²/a² - x²/b² = 1, what are the equations of the asymptotes?
A
y = ±(b/a)x
B
y = ±(a/b)x
C
y = ±a
D
x = ±b
Analysis & Theory
For y²/a² - x²/b² = 1, asymptotes are y = ±(a/b)x.