# 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 x^{2}/49 + y^{2}/36 = 1

**Solution:**

The given equation is x^{2}/49 + y^{2}/36 = 1

Here, the denominator of x^{2}/49 is greater than the denominator of y^{2}/36

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 = 7 and b = 6

Hence,

c = √a² - b²

= √49 - 36

= √13

Therefore,

The coordinates of the foci are (± √13, 0)

The coordinates of the vertices are (± 7, 0)

Length of major axis = 2a = 14

Length of minor axis = 2b = 12

Eccentricity, e = c/a = √13/7

Length of latus rectum = 2b^{2}/a = (2 × 36)/7 = 72/7

NCERT Solutions Class 11 Maths Chapter 11 Exercise 11.3 Question 5

## 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 x^{2}/49 + y^{2}/36 = 1

**Solution:**

The coordinates of the foci and vertices are (± √13, 0), (± 7, 0) respectively. The length of the major axis, minor axis, and latus rectum are 14, 12, 72/7 respectively

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