hyperbolas 4

Question

Find the vertices and foci of the hyperbola with equation  = 1

Answer 1

The hyperbola equation is (x - 5)² /81- (y - 1)² /144 = 1.

The standard form of the equation of a hyperbola with center (h, k) (where a and b are not equals to 0) is (x - h)²/a² - (y - k)²/b² = 1 (Transverse axis is horizontal) or (y - k)²/a² - (x - h)²/b² = 1 (Transverse axis is vertical).

Compare the equation (x - 5)² /81- (y - 1)² /144 = 1 with (x - h)²/a² - (y - k)²/b² = 1.

a² = 81, b² = 144, h = 5 and k = 1.

a = ± 9 and b = ± 12.

To find the value of c, substitute the value of a² = 81 and b² = 144 in b² = c² - a².

144 = c² - 81

225 = c²

c = ± 15.

Center = (h, k) = (5, 1),

Vertices = (h ± a, k) = (5 ± 9, 1) = (14, 1) and (- 4, 1),

Foci = (h ± c, k) = (5 ± 15, 1) = (20, 1) and (- 10, 1).