Find the equation for the ellipse that satisfies the given conditions b = 3, c = 4, centre at the origin; foci on the x axis.

Asked by Pragya Singh | 1 year ago |  102

Solution :-

b = 3, c = 4, centre at the origin and foci on the x axis.

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, b = 3 and c = 4.

It is known that a2 = b+ c2.

a2 = 3+ 42

= 9 + 16

=25

a =$$\sqrt{25}$$

= 5

The equation of the ellipse is $$\dfrac{x^2}{5^2}+ \dfrac{y^2}{3^2}=1$$

or $$\dfrac{x^2}{25}+ \dfrac{y^2}{9}=1$$

Answered by Abhisek | 1 year ago

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