Find the equation for the ellipse that satisfies the given conditions  Vertices (± 6, 0), foci (± 4, 0)

Asked by Pragya Singh | 1 year ago |  105

##### Solution :-

Vertices (± 6, 0) and foci (± 4, 0)

Here, the vertices are on the x-axis.

So, the equation of the ellipse will be of the form

$$\dfrac{x^2}{a^2}$$ +$$\dfrac{y^2}{b^2}$$ = 1, where ‘a’ is the semi-major axis.

Then, a = 6 and c = 4.

It is known that a2 = b+ c2.

62 = b2+42

36 = b2 + 16

b2 = 36 – 16

b = $$\sqrt{20}$$

The equation of the ellipse is $$\dfrac{x^2}{62}+\dfrac{y^2}{(\sqrt{20})^2}=1$$

or $$\dfrac{x^2}{62}+\dfrac{y^2}{20}=1$$

Answered by Abhisek | 1 year ago

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