The center of a hyperbola is (−5,8). The length of the conjugate axis is 6 units, and the length of the transverse axis is 14 units. The transverse axis is parallel to the y-axis. What is the equation of the hyperbola in standard form? Drag an expression to the boxes to correctly complete the equation.
a = 14/2 = 7 b = 6/2 = 3
Since the transverse axis is parallel to the y axis, we have this form
(y- k)^2 ( x - h)^2
_______ - ________ = 1 where (h, k) is the center
a^2 b^2
Filling in what we know
(y -8)^2 (x+ 5)^2
________ - _______ = 1 multiply through by 49*9 = 441
49 9
9( y^2 - 16y + 64) - 49 (x^2 + 10x + 25) = 441
9y^2 - 144y + 576 - 49x^2 - 490x - 1225 - 441 = 0
9y^2 - 49x^2 - 144y - 490x -1090 = 0