A.) A hyperbola with vertices (-5, 0) and (5, 0) has its centre at (0, 0) and the transverse axis is horizontal.
Therefore, the required equation is (x - 0)^2/5^2 - (y - 0)^2/6^2 = 1
x^2/25 - y^2/36 = 1
B.) A hyperbola with foci at (-1, 1) and (5, 1) and vertices at (0, 1) and (4, 1) has the center at (2, 1) and the transversal axis is horizontal. b^2 is given by 3^2 - 2^2 = 9 - 4 = 5.
Therefore, the required line is (x - 2)^2/2^2 - (y - 1)^2/5 = 1
(x - 2)^2/4 - (y - 1)^2/5 = 1
C.) A hyperbola with a center at (-5, -3), vertices at (-5, -5) and (-5, -1) and co-vertices at (-11, -3) and (1, -3) has a vertical transversal axis.
Therefore, the required equation is (y - (-3))^2/2^2 - (x - (-5))^2/6^2 = 1
(y + 3)^2/4 - (x + 5)^2/36 = 1
D.) A hyperbola with foci at (3, -3) and (3, 7) and vertices at (3, -1) and (3, 5) has its center at (3, 2) and a vertical transversal axis. b^2 is given by 5^2 - 3^2 = 25 - 9 = 16.
Therefore, the required equation is (y - 2)^2/3^2 - (x - 3)^2/16 = 1
(y - 2)^2/9 - (x - 3)^2/16 = 1
