Find the equation for the ellipse that satisfies the given conditions: Length of minor axis 16, foci (0, ±6).

Asked by Pragya Singh | 11 months ago |  96

Solution :-

Length of minor axis is 16 and foci (0, ±6).

Since the foci are on the y-axis, the major axis is along 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, 2b =16

b = 8 and c = 6.

It is known that a2 = b+ c2.

a2 = 8+ 62

= 64 + 36

=100

a = $$\sqrt{100}$$

= 10

The equation of the ellipse is $$\dfrac{x^2}{8^2}+ \dfrac{y^2}{10^2}=1$$

or $$\dfrac{x^2}{64}+ \dfrac{y^2}{100}=1$$

Answered by Abhisek | 11 months ago

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