Use the equation to do the following

Question

Use the equation (x-2)^2 / 81 - (y+1)^2 / 16 = 1 to find the following:

a. center

b. vertices

c. foci

d. asymptotes

d. graph

Answer 1

(x - 2)²/81 - (y + 2)²/16 = 1.

Compare the equation (x - 2)²/81 - (y + 2)²/16 = 1 with (x - h)²/a² - (y - k)²/b² = 1.

a² = 81, b² = 16, h = 2 and k = - 2

a = ± 9 and b = ± 4.

To find the value of c, substitute the value of a² = 81 and b² = 16 in b² = c² - a².

16 = c² - 81

97 = c²

c = ± √97.

Here the transverse axis is horizontal, the asymptotes are of the forms y = (b/a) x and y = - (b/a) x.

The asymptotes equations are y = ± 4/9 x.

The slopes of asymptotes are ± 4/9,

Center = (h, k) = (2, - 2),

Vertices = (h ± a, k) = (2 ± 9, -2) = (11, -2) and (- 7, -2),

Foci = (h ± c, k) = (2 ± √97, -2) = ( 2 + √97, -2) and (2 - √97, -2).