Final answer:
The standard form of the hyperbola with a conjugate axis of 20 can be represented as (x - h)²/a² - (y - k)²/b² = 1. To find the values of h and k, use the given points on the hyperbola (-2, -11).
Step-by-step explanation:
The standard form of the hyperbola with a conjugate axis of 20 can be represented as (x - h)²/a² - (y - k)²/b² = 1. To find the values of h and k, we use the given points on the hyperbola (-2, -11). The center of the hyperbola is (h, k), so in this case, h = -2 and k = -11. Plugging these values into the standard form equation, we get (x + 2)²/a² - (y + 11)²/b² = 1. To find the value of a, we use the length of the conjugate axis, which is 20. Since the conjugate axis is perpendicular to the transverse axis, the value of a is half the length of the conjugate axis. Therefore, a = 10. The equation can be simplified to (x + 2)²/100 - (y + 11)²/b² = 1.