Find the (i) leng

Given:

16x² + 25y² = 400

Divide by 400 to both the sides, we get

…(i)

Since, 25 > 4

So, above equation is of the form,

…(ii)

Comparing eq. (i) and (ii), we get

a² = 25 and b² = 4

⇒ a = √25 and b = √4

⇒ a = 5 and b = 2

(i) To find: Length of major axes

Clearly, a > b, therefore the major axes of the ellipse is along x axes.

∴Length of major axes = 2a

= 2 × 5

= 10 units

(ii) To find: Coordinates of the Vertices

Clearly, a > b

∴ Coordinate of vertices = (a, 0) and (-a, 0)

= (5, 0) and (-5, 0)

(iii) To find: Coordinates of the foci

We know that,

Coordinates of foci = (±c, 0) where c² = a² – b²

So, firstly we find the value of c

c² = a² – b²

= 25 – 4

c² = 21

c = √21 …(I)

∴ Coordinates of foci = (±√21, 0)

(iv) To find: Eccentricity

We know that,

[from (I)]

(v) To find: Length of the Latus Rectum

We know that,