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

16.  Find the equation for the ellipse that satisfies the given conditions:

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

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Given, In an ellipse,

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

Here, the focus of the ellipse is on the  Y-axis so the major axis of this ellipse will be Y-axis.

Therefore, the equation of the ellipse will be of the form:

$\frac{x^2}{b^2}+\frac{y^2}{a^2}=1$

Where $a$ and $b$are the length of the semimajor axis and semiminor axis respectively.

So on comparing standard parameters( length of semi-minor axis and foci) with the given one, we get

$2b=16\Rightarrow b=8$ and $c=6$

Now, As we know the relation,

$a^2=b^2+c^2$

$a=\sqrt{b^2+c^2}$

$a=\sqrt{8^2+6^2}$

$a=\sqrt{64+36}$

$a=\sqrt{100}$

$a=10$

Hence, The Equation of the ellipse will be :

$\frac{x^2}{8^2}+\frac{y^2}{10^3}=1$

Which is

$\frac{x^2}{64}+\frac{y^2}{100}=1$.

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