Find the coordinates of the foci and the vertices, the eccentricity, and the length of the latus rectum of the hyperbola x²/16 - y²/9 = 1

Solution:

The given equation is x²/16 - y²/9 = 1

On comparing this equation with the standard equation of hyperbola

i.e., x²/a² - y²/b² = 1, we obtain

a = 4 and b = 3.

We know that, c² = a² + b²

Hence,

⇒ c² = 4² + 3²

⇒ c² = 25

⇒ c = 5

Therefore,

The coordinates of the foci are (± 5, 0)

The coordinates of the vertices are (± 4, 0)

Eccentricity, e = c/a = 5/4

Length of latus rectum = 2b²/a = (2 × 9)/4 = 9/2

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NCERT Solutions Class 11 Maths Chapter 11 Exercise 11.4 Question 1

Find the coordinates of the foci and the vertices, the eccentricity, and the length of the latus rectum of the hyperbola x²/16 - y²/9 = 1

Summary:

The coordinates of the foci and vertices of the hyperbola x²/16 - y²/9 = 1 are (± √5, 0), (± 4, 0) respectively. The length of the latus rectum is 9/2