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 4x2 + 9y2 = 36

Asked by Pragya Singh | 1 year ago |  92

Solution :-

The equation is 4x2 + 9y2 = 36

or $$\dfrac{x^2}{9}$$ + $$\dfrac{y^2}{4}$$ = 1 or $$\dfrac{x^2}{3^2}$$+ $$\dfrac{y^2}{2^2}$$ = 1

Here, the denominator of $$\dfrac{x^2}{3^2}$$ is greater than the denominator of $$\dfrac{y^2}{2^2}$$.

So, the major axis is along the x-axis, while the minor axis is along the y-axis.

On comparing the given equation with

$$\dfrac{x^2}{a^2}$$ +$$\dfrac{y^2}{b^2}$$ = 1, we get

a =3 and b =2.

c = $$\sqrt{ (a^2 – b^2)}$$

$$\sqrt{ (9– 4)}$$

=$$\sqrt{5}$$

Then,

The coordinates of the foci are ($$\sqrt{5}$$, 0) and ($$-\sqrt{5}$$, 0).

The coordinates of the vertices are (3, 0) and (-3, 0)

Length of major axis = 2a = 2 (3) = 6

Length of minor axis = 2b = 2 (2) = 4

Eccentricity, e = $$\dfrac{c}{a}$$$$\dfrac{\sqrt{5}}{3}$$

Length of latus rectum = $$\dfrac{2b^2}{a}$$

= $$\dfrac{(2×2^2)}{3}$$ = $$\dfrac{(2×4)}{3}$$$$\dfrac{8}{3}$$

Answered by Abhisek | 1 year ago

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