Answer:
The equation of the hyperbola is x²/60² - y²/11² = 1 ⇒ 1st answer
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
* Where:
# 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)
* Now from the graph
- The center of the hyperbola is (0 , 0)
- The vertices of the hyperbola are (-60 , 0) and (60 , 0)
∴ a = ± 60
∴ a² = 60²
- The co-vertices of the hyperbola are (0 , -11) and (0 , 11)
∴ b = ± 11
∴ b² = 11²
* Substitute the values of a² and b² in the form of the equation
∴ x²/60² - y²/11² = 1
* The equation of the hyperbola is x²/60² - y²/11² = 1