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 x²/49 + y²/36 = 1

Solution:

The given equation is x²/49 + y²/36 = 1

Here, the denominator of x²/49 is greater than the denominator of y²/36

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

On comparing the given equation with

x²/a² + y²/b² = 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 = 2b²/a = (2 × 36)/7 = 72/7

NCERT Solutions Class 11 Maths Chapter 11 Exercise 11.3 Question 5