Question

Find the coordinates of the foci and the vertices, the eccentricity, and the length of the latus rectum of the hyperbola y²/9 - x²/27=1

Answer 1

The given equation is    Y²/9 - X²/27=1 or Y²/3² -X²/( √27)² =1

On comparing this equation with the standard equation of hyperbola Y²/a² - X²/b² =1 i.e.,,

we obtain a = 3 and b=√27

We know that a² + b² = C².

∴C² = 3² + (√27)² =9+27 =36

⇒ C = 6

Therefore,
The coordinates of the foci are (0, ±6).
The coordinates of the vertices are (0, ±3).