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

Solution:

The given equation is

y²/9 - x²/27 = 1

On comparing this equation with the standard equation of hyperbola

i.e., y²/a² - x²/b² = 1, we obtain

a = 3 and b = √27.

We know that, c² = a² + b²

Hence,

⇒ c² = 3² + (√27)²

⇒ c² = 9 + 27

⇒ c² = 36

⇒ c = 6

Therefore,

The coordinates of the foci are (0, ± 6)

The coordinates of the vertices are (0, ± 3)

Eccentricity, e = c/a = 6/3 = 2

Length of latus rectum = 2b²/a = (2 × 27)/3 = 18

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NCERT Solutions Class 11 Maths Chapter 11 Exercise 11.4 Question 2

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

Summary:

The coordinates of the foci and vertices of the hyperbola y²/9 - x²/27 = 1 are (0, ± 6), (0, ± 3) respectively. The length of the latus rectum is 18