+309 The center of a hyperbola is (1,4) . The length of the conjugate axis is 16 units, and the length of the transverse axis is 20 units. The transverse axis is parallel to the y-axis.
What is the equation of the hyperbola in standard form?
+128474 Since the transverse axis is parallel to the y axis, we have this form
(y - k)^2 (x - h)^2
_______ - ________ = 1
a^2 b^2
(h, k) is the center (1,4)
a = 20/2 = 10 ⇒ a^2 = 100
b = 16/2 = 8 ⇒ b^2 = 64.we have
(y - 4)^2 ( x - 1)^2
_______ - ________ = 1
100 64
Here's a graph : https://www.desmos.com/calculator/mkgqzex2ft
