hyperbolas 3

Question

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

Answer 1

The hyperbola equation is x²/4 - y²/60 = 1.

The standard form of the equation of a hyperbola with center at the origin (where a and b are not equals to 0) is x²/a² - y²/b² = 1 (Transverse axis is horizontal) or y²/a² - x²/b² = 1 (Transverse axis is vertical).

The vertices and foci are, respectively a and c units from the center and the relation between a, b and c is b² = c² - a².

Compare the equation x²/4 - y²/60 = 1. with x²/a² - y²/b² = 1.

a² = 4 and b² = 60

a = ± 2 and b = ± √60 =± 2√15 

To find the value of c, substitute the value of a² = 2 and b² = 60 in b² = c² - a².

60 = c² - 2

62 = c²

c = ± √62.

Vertices = (± 2, 0) = (± 2, 0)

Foci = (± c, 0) = (± √62, 0)