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