Find the equation for the ellipse that satisfies the given conditions Foci (±3, 0), a = 4

Asked by Pragya Singh | 11 months ago |  95

##### Solution :-

Foci (±3, 0) and a = 4

Since the foci are on the x-axis, the major axis is along 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, c = 3 and a = 4.

It is known that a2 = b+ c2.

a2 = 8+ 62

= 64 + 36

= 100

16 = b2 + 9

b2 = 16 – 9

= 7

The equation of the ellipse is $$\dfrac{x^2}{16}+ \dfrac{y^2}{7}=1$$

Answered by Abhisek | 11 months ago

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