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 36x² + 4y² = 144

Solution:

The given equation is

36x² + 4y² = 144

It can be written as,

36x² + 4y² = 144

⇒ x²/4 + y²/36 = 1

⇒ x²/(2)² + y²/(6)² = 1

Here, the denominator of y²/ (6)² is greater than the denominator of x²/ (2)²

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 = 2 and a = 6

Hence,

c = √36 - 4

= √32

= 4√2

Therefore,

The coordinates of the foci are (0, ± 4√2)

The coordinates of the vertices are (0 ± 6)

Length of major axis = 2a = 12

Length of minor axis = 2b = 4

Eccentricity, e = c/a = 4√2/6 = 2√2/3

Length of latus rectum = 2b²/a = (2 × 4)/6 = 4/3

NCERT Solutions Class 11 Maths Chapter 11 Exercise 11.3 Question 7