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

      Vertices (± 6, 0), foci (± 4, 0)

Answers (1)

Given, In an ellipse, 

 Vertices (± 6, 0), foci (± 4, 0)

Here Vertices and focus 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=6 and c=4

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{6^2-4^2}

b=\sqrt{36-16}

b=\sqrt{20}

Hence, The Equation of the ellipse will be :

\frac{x^2}{6^2}+\frac{y^2}{(\sqrt{20})^2}=1

Which is 

\frac{x^2}{36}+\frac{y^2}{20}=1.

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