Find the equation for the ellipse that satisfies the given conditions: Vertices (0, ± 13), foci (0, ± 5)

Asked by Pragya Singh | 1 year ago |  121

Solution :-

Vertices (0, ± 13) and foci (0, ± 5)

Here, the vertices are on the y-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 =13 and c = 5.

It is known that a2 = b+ c2.

132 = b2+52

169 = b2 + 15

b2 = 169 – 125

b = $$\sqrt{144}$$

= 12

The equation of the ellipse is  $$\dfrac{x^2}{12^2}$$$$\dfrac{y^2}{13^2}$$ = 1

or $$\dfrac{x^2}{144}$$ + $$\dfrac{y^2}{169}$$ = 1

Answered by Abhisek | 1 year ago

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