Question

The vertices of a hyperbola are located at (3, −6) and (3, 6). The foci of the same hyperbola are located at (3,−10) and (3, 10). What is the equation of the hyperbola? = 1 = 1 = 1 = 1

Answer 1

The answer is A

Explanation:

Cuz maf

Answer 2

The equation of the hyperbola with the given vertices and foci is gotten as; x²/9 - y²/40

What is the Equation of the Hyperbola?

The distance between the two vertices since they have the same x-coordinate is;

Vertices distance = 6 - (-6) = 12

2a = 6

Thus;

a = 3

Distance between vertex and Focus = 10 - 6 = 4

Thus;

a(e - 1) = 4

(e - 1) = 4/3

e = 1 + 4/3

e = 7/3

Now, b = a√(e² - 1)

b = 3√((7/3)² - 1)

b = 3√(40/9)

b² = 40

Equation of hyperbola is;

x²/a² - y²/b²

Thus;

x²/9 - y²/40

Read more about equation of hyperbola at;