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 x²/25 + y²/100 = 1

Solution:

The given equation is x²/25 + y²/100 = 1

Here, the denominator of y/100 is greater than the denominator of x/25

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

On comparing the given equation with

x²/ b² + y²/a² = 1 we obtain b = 5 and a = 10

Hence,

c = √a² - b²

= √100 - 25

= √75

= 5√3

Therefore,

The coordinates of the foci are (0, ± 5√3)

The coordinates of the vertices are (0, ± 10)

Length of major axis = 2a = 20

Length of minor axis = 2b = 10

Eccentricity, e = c/a = 5√3/10

Length of latus rectum = 2b²/a = (2 × 25)/10 = 5

NCERT Solutions Class 11 Maths Chapter 11 Exercise 11.3 Question 4