Answer :

Given:

3x^{2} + 2y^{2} = 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

a^{2} = 9 and b^{2} = 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 c^{2} = a^{2} – b^{2}

So, firstly we find the value of c

c^{2} = a^{2} – b^{2}

= 9 – 6

c^{2} = 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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