# Find the (i) leng

Given:

3x2 + 2y2 = 18

Divide by 18 to both the sides, we get

…(i)

Since, 6 < 9

So, above equation is of the form,

…(ii)

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

a2 = 9 and b2 = 6

a = √9 and b = √6

a = 3 and b = √6

(i) To find: Length of major axes

Clearly, a < b, therefore the major axes of the ellipse is along y axes.

Length of major axes = 2a

= 2 × 3

= 6 units

(ii) To find: Coordinates of the Vertices

Clearly, a > b

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

= (0, 6) and (0, -6)

(iii) To find: Coordinates of the foci

We know that,

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

So, firstly we find the value of c

c2 = a2 – b2

= 9 – 6

c2 = 3

c = √3 …(I)

Coordinates of foci = (0, ±√3)

(iv) To find: Eccentricity

We know that,

[from (I)]

(v) To find: Length of the Latus Rectum

We know that,

= 4

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