# Find the coordinates of the foci and the vertices, the eccentricity, and the length of the latus rectum of the hyperbola 9*y*^{2} - 4*x*^{2} = 36

**Solution:**

The given equation is 9y^{2} - 4x^{2} = 36

It can be written as

9y^{2} - 4x^{2} = 36

y^{2}/4 - x^{2}/9 = 1

y^{2}/2^{2} - x^{2}/3^{2} = 1 ....(1)

On comparing this equation with the standard equation of hyperbola

i.e., x^{2}/a^{2} + y^{2}/b^{2} = 1, we obtain

a = 2 and b = 3.

We know that, c^{2} = a^{2} + b^{2}

Hence,

⇒ c^{2} = 2^{2} + 3^{2}

⇒ c^{2} = 4 + 9

⇒ c^{2} = 13

⇒ c = √13

Therefore,

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

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

Eccentricity, e = c/a = √13/2

Length of latus rectum = 2b^{2}/a = (2 × 9)/2 = 9

NCERT Solutions Class 11 Maths Chapter 11 Exercise 11.4 Question 3

## Find the coordinates of the foci and the vertices, the eccentricity, and the length of the latus rectum of the hyperbola 9*y*^{2} - 4*x*^{2} = 36

**Summary:**

The coordinates of the foci and vertices of the hyperbola 9y^{2} - 4x^{2} = 36 are (0, ± √13), (0, ± 2) respectively. The length of the latus rectum is 9