Question

Find the coordinates of the foci and the vertices, the eccentricity, and the length of the latus rectum of the hyperbola 9y² – 4x² = 36

Answer 1

The given equation is 9y² – 4x² = 36.
It can be written as
9y² – 4x² = 36

On comparing equation (1) with the standard equation of hyperbola Y²/a² - X²/b²=1 i.e.,, we obtain a = 2 and b = 3.
We know that a² + b² = c².

∴ C² =4+9=13

⇒C =√13

Therefore,

The coordinates of the foci are (0,± √13)
The coordinates of the vertices are  (0, ± 2)