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 x²/16 + y²/9 = 1

Solution:

The given equation is x²/16 + y²/9 = 1

Here, the denominator of x²/16 is greater than the denominator of y²/ 9

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 = 4 and b = 3

Hence,

c = √a² - b²

= √16 - 9

= √7

Therefore,

The coordinates of the foci are (± √7, 0)

The coordinates of the vertices are (0, ± 4)

Length of major axis = 2a = 8

Length of minor axis = 2b = 6

Eccentricity, e = c/a = √7/4

Length of latus rectum = 2b²/a = (2 × 9)/4 = 9/2

NCERT Solutions Class 11 Maths Chapter 11 Exercise 11.3 Question 3