Question

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^2/16+y^2/9=1​

Answer 1

Answer:

Given :

Equation of ellipse :

x² / 16 + y² / 9 = 1

= > x² / 4² + y² / 3² = 1

We have standard equation of ellipse :

i.e. x² / a² + y² / b² = 1

On comparing we get :

a = 4 and b = 3

We know :

a² = b² + c²

c = √ ( a² - b² )

c = √ 7

Now coordinate of foci ( ± c , 0)

=  > c ( ± √ 7 , 0 )

Vertices ( ± a , 0 )

= > ( ± 4 , 0 )

Length of major axis = 2 a

= > 8

Length of minor axis = 2 b

= > 6

Eccentricity e = c / a

e = √ 7 / 4

Length of lotus rectum = 2 b² / a

= > 2 × 9 / 4

= > 9 / 2  .

Hence we get answer.