Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse 16x² + y² = 16

Solution:

The given equation is 16x² + y² = 16

It can be written as,

16x² + y² = 16

⇒ x²/1 + y²/16 = 1 [ Dividing both sides by 16 ]

⇒ x²/ (1)² + y²/ (4)² = 1

Here, the denominator of y²/(4)² is greater than the denominator of x²/(1)²

Therefore, the major axis is along the y-axis, while the minor axis is along the x-axis.

On comparing the given equation with

x²/b² + y²/a² = 1 we obtain b = 1 and a = 4

Hence,

c = √a² - b²

c = √16 - 1

= √15

Therefore,

The coordinates of the foci are (0, ±√15)

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

Length of major axis = 2a = 8

Length of minor axis = 2b = 2

Eccentricity, e = c/a = √15/4

Length of latus rectum = 2b²/a = (2 × 1)/4 = 1/2

NCERT Solutions Class 11 Maths Chapter 11 Exercise 11.3 Question 8