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

Solution:

The given equation is 9y² - 4x² = 36

It can be written as

9y² - 4x² = 36

y²/4 - x²/9 = 1

y²/2² - x²/3² = 1 ....(1)

On comparing this equation with the standard equation of hyperbola

i.e., x²/a² + y²/b² = 1, we obtain

a = 2 and b = 3.

We know that, c² = a² + b²

Hence,

⇒ c² = 2² + 3²

⇒ c² = 4 + 9

⇒ c² = 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 = 2b²/a = (2 × 9)/2 = 9

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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 9y² - 4x² = 36

Summary:

The coordinates of the foci and vertices of the hyperbola 9y² - 4x² = 36 are (0, ± √13), (0, ± 2) respectively. The length of the latus rectum is 9