12.1k views
3 votes
The foci for the hyperbola (y-2)²/16 - (x-1)²/144 = 1 are (-1, 2 + 4√10) and (-1, 2 - 4√10). True or False?

a) True
b) False

1 Answer

2 votes

Final answer:

The given foci for the hyperbola are incorrect because the correct foci should have an x-coordinate of 1, not -1. The correct foci are (1, 2 ± 4√10). Thus, the statement is False.

Step-by-step explanation:

The question asks whether the given foci (-1, 2 + 4√10) and (-1, 2 - 4√10) are true for the hyperbola with the equation (y-2)²/16 - (x-1)²/144 = 1. To determine the correctness of this statement, we need to understand the general form of the hyperbola equation and how the foci are calculated.

For a hyperbola centered at (h, k) with a vertical transverse axis, the general form is (y-k)²/a² - (x-h)²/b² = 1. The distance between the center and the foci along the vertical transverse axis is denoted c, where c is found using the equation c² = a² + b².

In the given equation, a² = 16 and b² = 144, so c is calculated as c = √(16 + 144) = √160 = 4√10. The center of the hyperbola is at (h, k) = (1, 2). Therefore, the foci should be at (1, 2 ± 4√10), which means that the given foci are incorrect because the x-coordinate should be 1, not -1. Hence, the statement is False.

User Red Fx
by
7.5k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories