# 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 4x^{2} + 9y^{2} = 36

**Solution:**

The given equation is 4x^{2} + 9y^{2} = 36

It can be written as,

4x^{2} + 9y^{2} = 36

⇒ x^{2}/9 + y^{2}/4 = 1 [ Dividing both sides by 36 ]

⇒ x^{2 }/ (3)^{2} + y^{2 }/ (2)^{2} = 1

Here, the denominator of x^{2}/(3)^{2} is greater than the denominator of y^{2}/(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

x^{2}/a^{2} + y^{2}/b^{2} = 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 = 2b^{2}/a = (2 × 4)/3 = 8/3

NCERT Solutions Class 11 Maths Chapter 11 Exercise 11.3 Question 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 4x^{2} + 9y^{2} = 36

**Summary:**

The coordinates of the foci and vertices of the ellipse 4x^{2} + 9y^{2} = 36 are (± √5, 0), (± 3, 0) respectively. The length of the major axis, minor axis, and latus rectum are 6, 4, 8/3, respectively

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