# Find the (i) leng

Given:

…(i)

Since, 25 > 9

So, above equation is of the form,

…(ii)

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

a2 = 25 and b2 = 9

a = √25 and b = √9

a = 5 and b = 3

(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 – 9

c2 = 16

c = √16

c = 4 …(I)

Coordinates of foci = (±4, 0)

(iv) To find: Eccentricity

We know that,

[from (I)]

(v) To find: Length of the Latus Rectum

We know that,

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