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

       Foci (± 3, 0), a = 4

Answers (1)

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 bare 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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