Find the coordinates of the foci and the vertices, the eccentricity, and the length of the latus rectum of the hyperbola 49y² - 16x² = 784

Solution:

The given equation is 49y² - 16x² = 784

It can be written as

49y² - 16x² = 784

y²/16 - x²/49 = 1

y²/4² - x²/7² = 1 ....(1)

On comparing this equation with the standard equation of hyperbola

i.e., x²/a² + y²/b² = 1, we obtain

a = 4 and b = 7.

We know that, c² = a² + b²

Hence,

⇒ c² = (4)² + (7)²

⇒ c² = 16 + 49

⇒ c² = 65

⇒ c = √65

Therefore,

The coordinates of the foci are (0, ± √65)

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

Eccentricity, e = c/a = √65/4

Length of latus rectum = 2b²/a = (2 × 49)/4 = 49/2

NCERT Solutions Class 11 Maths Chapter 11 Exercise 11.4 Question 6