Question

If the lengths of the transverse axis and the latus rectum of a hyperbola are 6 and `8/3` respectively, then the equation of the hyperbola is ______.

Options

• 4x² - 9y² = 72

• 4x² - 9y² = 36

• 9x² - 4y² = 72

• 9x² - 4y² = 36

Answer 1

If the lengths of the transverse axis and the latus rectum of a hyperbola are 6 and `8/3` respectively, then the equation of the hyperbola is 4x² - 9y² = 36.

Explanation:

We have,

Length of transverse axis 2a = 6 ⇒ a = 3

and length of latus rectum, `"2b"^2/"a" = 8/3`

`=> 2"b"^2 = 8/3 xx 3 = 8 = "b"^2 = 4`

∴ Required equation of hyperbola is

`x^2/"a"^2 - "y"^2/"b"^2 = 1`

`=> x^2/9 - "y"^2/4 = 1`

⇒ 4x² - 9y² = 36