Answer:
(x - 3)²/3² - (y + 4)²/2² = 1 ⇒ (0 , -4) , (6 , -4)
(x - 4)²/7² - (y + 6)²/5² = 1 ⇒ (-3 , -6) , (11 , -6)
(y + 5)²/5² - (x - 4)²/8² = 1 ⇒ (4 , 0) , (4 , -10)
(y + 7)²/7² - (x + 2)²/4² = 1 ⇒ (-2 , 0) , (-2 , -14)
(x + 1)²/9² - (y - 1)²/11² = 1 ⇒ (8 , 1) , (-10 , 1)
Step-by-step explanation:
* Lets revise the standard form of the equations of the hyperbola
- The standard form of the equation of a hyperbola with center (h , k)
and transverse axis parallel to the x-axis is (x - h)²/a² - (y - k)²/b² = 1
- The coordinates of the vertices are (h ± a , k)
- The standard form of the equation of a hyperbola with center (h , k)
and transverse axis parallel to the y-axis is (y - k)²/a² - (x - h)²/b² = 1
- The coordinates of the vertices are (h , k ± a)
* Lets solve the problem
# (x - 3)²/3² - (y + 4)²/2² = 1
∵ (x - h)²/a² - (y - k)²/b² = 1
∴ a = 3 , b = 2 , h = 3 , k = -4
∵ The coordinates of the vertices are (h ± a , k)
∴ The coordinates of the vertices are (3 - 3 , -4) , (3 + 3 , -4)
∴ The coordinates of the vertices are (0 , -4) , (6 , -4)
* (x - 3)²/3² - (y + 4)²/2² = 1 ⇒ (0 , -4) , (6 , -4)
# (y - 1)²/2² - (x - 7)²/6² = 1
∵ (y - k)²/a² - (x - h)²/b² = 1
∴ a = 2 , b = 6 , h = 7 , k = 1
∵ The coordinates of the vertices are (h , k ± a)
∴ The coordinates of the vertices are (7 , 1 - 2) , (7 , 1 + 2)
∴ The coordinates of the vertices are (7 , -1) , (7 , 3)
* No answer for this equation
# (x - 4)²/7² - (y + 6)²/5² = 1
∵ (x - h)²/a² - (y - k)²/b² = 1
∴ a = 7 , b = 5 , h = 4 , k = -6
∵ The coordinates of the vertices are (h ± a , k)
∴ The coordinates of the vertices are (4 - 7 , -6) , (4 + 7 , -6)
∴ The coordinates of the vertices are (-3 , -6) , (11 , -6)
* (x - 4)²/7² - (y + 6)²/5² = 1 ⇒ (-3 , -6) , (11 , -6)
# (y + 5)²/5² - (x - 4)²/8² = 1
∵ (y - k)²/a² - (x - h)²/b² = 1
∴ a = 5 , b = 8 , h = 4 , k = -5
∵ The coordinates of the vertices are (h , k ± a)
∴ The coordinates of the vertices are (4 , -5 + 5) , (4 , -5 - 5)
∴ The coordinates of the vertices are (4 , 0) , (4 , -10)
* (y + 5)²/5² - (x - 4)²/8² = 1 ⇒ (4 , 0) , (4 , -10)
# (y + 7)²/7² - (x + 2)²/4² = 1
∵ (y - k)²/a² - (x - h)²/b² = 1
∴ a = 7 , b = 4 , h = -2 , k = -7
∵ The coordinates of the vertices are (h , k ± a)
∴ The coordinates of the vertices are (-2 , -7 + 7) , (-2 , -7 - 7)
∴ The coordinates of the vertices are (-2 , 0) , (-2 , -14)
* (y + 7)²/7² - (x + 2)²/4² = 1 ⇒ (-2 , 0) , (-2 , -14)
# (x + 1)²/9² - (y - 1)²/11² = 1
∵ (x - h)²/a² - (y - k)²/b² = 1
∴ a = 9 , b = 11 , h = -1 , k = 1
∵ The coordinates of the vertices are (h ± a , k)
∴ The coordinates of the vertices are (-1 + 9 , 1) , (-1 - 9 , 1)
∴ The coordinates of the vertices are (8 , 1) , (-10 , 1)
* (x + 1)²/9² - (y - 1)²/11² = 1 ⇒ (8 , 1) , (-10 , 1)
