The center of a hyperbola is (-3,2). The length of the conjugate axis is 12 units, and the length of the transverse axis is 8 units. The

transverse axis is parallel to the y-axis.

What is the equation of the hyperbola in standard form?

(y - 2) ² / 16 - (x + 3) ² / 36 = 1

Step-by-step explanation:

The conjugate axis is the axis of symmetry. The transverse axis is the line connecting the vertices of the hyperbola. Since the transverse axis is parallel to the y-axis, this is a vertical hyperbola:

(y - k) ² / a² - (x - h) / b² = 1

where (h, k) is the center of the hyperbola, a is half the length of the transverse axis, and b is half the length of the conjugate axis.

Here, the center is (-3, 2), a = 8/2 = 4, and b = 12/2 = 6.

(y - 2) ² / 16 - (x + 3) ² / 36 = 1