Find the equation for the ellipse that satisfies the given conditions Length of major axis 26, foci (±5, 0)

Asked by Pragya Singh | 11 months ago |  107

Solution :-

Length of major axis is 26 and foci (±5, 0)

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, 2a = 26

a = 13 and c = 5.

It is known that a2 = b+ c2.

132 = b2+52

169 = b2 + 25

b2 = 169 – 25

b =$$\sqrt{144}$$

= 12

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

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

Answered by Abhisek | 11 months ago

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