Question

The equation y²/8² - x²/b² represents a hyperbola centered at the origin with a focus of (0, -10).

What is the value of b?

4
6
10
12

Answer 1

Answer: 6

Explanation:

Answer 2

b = 6

Explanation:

You probably already know the general equation from the my last couple of answer.

In this question, we have:

a=8

b= ?

c= -10 , c is the value of the foci

surprisingly, you can solve the value for a, b, and c using the same equation as the Pythagorean theorem.

c² = a² + b²

we need to solve for b so lets rearrange the equation.

b² = c² - a²

b = ±√(c² - a²)

b = ±√((-10)² - (8)²)

b = ±√((-10)² - (8)²)

b = ±√(100 - 64)

b = ±√(36)

b = ±6

b = 6