# 17.  Find the equation for the ellipse that satisfies the given conditions:       Foci (± 3, 0), a = 4

Given, In an ellipse,

V Foci (± 3, 0), a = 4

Here foci of the ellipse are in X-axis so the major axis of this ellipse will be X-axis.

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

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

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

So on comparing standard parameters( vertices and foci) with the given one, we get

$a=4$ and $c=3$

Now, As we know the relation,

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

$b^2=a^2-c^2$

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

$b=\sqrt{4^2-3^2}$

$b=\sqrt{7}$

Hence, The Equation of the ellipse will be :

$\frac{x^2}{4^2}+\frac{y^2}{(\sqrt{7})^2}=1$

Which is

$\frac{x^2}{16}+\frac{y^2}{7}=1$.

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