Find the center and vertices of the hyperbola. $12 x ^ { 2 } - 4 y ^ { 2 } - 72 x - 16 y + 44 = 0$
A)center: (3,-2),vertices: (3,-4), (3,0)
B)center: (-3,2),vertices: (-3,0), (-3,4)
C)center: (3,-2),vertices: (1,-2), (5,-2)
D)center: (2,-3),vertices: (0,-3), (4,-3)
E)center: (-3,2),vertices: (-5,2), (-1,2)

Question

Quizplus · Accepted Answer

A hyperbola has its center at (h,k), and its vertices lie on the major axis, which is either horizontal or vertical.
The given vertices are (1,-2), and (5,-2). Since they are both on the same horizontal line, the major axis is horizontal. Therefore, the center is the midpoint of the line joining the vertices, which is (3,-2). The vertices on this horizontal major axis are (1,-2) and (5,-2), so the answer is choice C.

Find the Center and Vertices of the Hyperbola 12x2−4y2−72x−16y+44=012 x ^ { 2 } - 4 y ^ { 2 } - 72 x - 16 y + 44 = 012x2−4y2−72x−16y+44=0

Find the Center and Vertices of the Hyperbola $12 x ^ { 2 } - 4 y ^ { 2 } - 72 x - 16 y + 44 = 0$