Question

Which of the following is the equation of a hyperbola with center at (0, 0), with a = 4, b = 1, opening horizontally?

Answer 1

Answer:

The equation of the hyperbola is x²/16 - y²/1 = 1

Step-by-step explanation:

* Lets study the equation of the hyperbola

- The standard form of the equation of a hyperbola with  

  center (0 , 0) and transverse axis parallel to the x-axis is

  x²/a² - y²/b² = 1

# The length of the transverse axis is 2a

# The coordinates of the vertices are (±a , 0)

# The length of the conjugate axis is 2b

# The coordinates of the co-vertices are (0 , ±b)

# The coordinates of the foci are (± c , 0),  

# The distance between the foci is 2c where c² = a² + b²

* Now lets solve the problem

∵ The center of the hyperbola is (0 , 0)

∵ It is opening horizontally

∴ x²/a² - y²/b² = 1

∵ a = 4 , b = 1

∴ a² = (4)² = 16

∴ b² = (1)² = 1

∴ x²/16 - y²/1 = 1

∴ The equation of the hyperbola is x²/16 - y²/1 = 1