Find the coordinates of the foci and the vertices, the eccentricity, and the length of the latus rectum of the hyperbola 16x² - 9y² = 576

Solution:

The given equation is 16x² - 9y² = 576

It can be written as

16x² - 9y² = 576

x²/ 36 - y²/ 64 = 1

x²/6² - y²/ 8² = 1 ....(1)

On comparing this equation with the standard equation of hyperbola

i.e., x²/a² + y²/b² = 1, we obtain

a = 6 and b = 8.

We know that, c² = a² + b²

Hence,

⇒ c² = 6² + 8²

⇒ c² = 36 + 64

⇒ c² = 100

⇒ c = 10

Therefore,

The coordinates of the foci are (± 10, 0)

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

Eccentricity, e = c/a = 10/6 = 5/3

Length of latus rectum = 2b²/a = (2 × 64)/6 = 64/3

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NCERT Solutions Class 11 Maths Chapter 11 Exercise 11.4 Question 4

Find the coordinates of the foci and the vertices, the eccentricity, and the length of the latus rectum of the hyperbola 16x² - 9y² = 576.

Solution:

The coordinates of the foci and vertices of the hyperbola 16x² - 9y² = 576 are (± 10, 0), (± 6, 0) respectively. The length of the latus rectum is 64/3