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 4x² + 9y² = 36

Solution:

The given equation is 4x² + 9y² = 36

It can be written as,

4x² + 9y² = 36

⇒ x²/9 + y²/4 = 1 [ Dividing both sides by 36 ]

⇒ x²/ (3)² + y²/ (2)² = 1

Here, the denominator of x²/(3)² is greater than the denominator of y²/(2)²

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 = 3 and b = 2

Hence,

c = √a² - b²

c = √9 - 4

= √5

Therefore,

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

The coordinates of the vertices are (± 3, 0)

Length of major axis = 2a = 6

Length of minor axis = 2b = 4

Eccentricity, e = c/a = (√ 5 / 3)

Length of latus rectum = 2b²/a = (2 × 4)/3 = 8/3

NCERT Solutions Class 11 Maths Chapter 11 Exercise 11.3 Question 9