In each of the Exercises 1 to 9, 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 x² / 36 + y² / 16 = 1

Solution:

The given equation is x²/36 + y²/16 = 1

Here, the denominator of x²/36 is greater than the denominator of y²/16

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

On comparing the given equation with x²/a² + y²/b² = 1 we obtain a = 6 and b = 4

Hence,

c = √a² - b²

= √36 - 16

= √20

= 2√5

Therefore,

The coordinates of the foci are (± 2√5, 0)

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

Length of major axis = 2a = 12

Length of minor axis = 2b = 8

Eccentricity, e = c/a = 2√5/6 = √5/3

Length of latus rectum = (2b²)/a = (2 × 16)/6 = 16/3

---

NCERT Solutions Class 11 Maths Chapter 11 Exercise 11.3 Question 1

In each of the Exercises 1 to 9, 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.x² / 36 + y² / 16 = 1

Summary:

The coordinates of the foci and vertices are (± 2√5, 0), (± 6, 0) respectively. The length of the major axis, minor axis, and latus rectum are 12, 8, 16/3 respectively