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Find the equation for the ellipse that satisfies the given conditions: Ends of major axis (± 3, 0), ends of minor axis (0, ± 2)

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

       Ends of major axis (± 3, 0), ends of minor axis (0, ± 2)

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Given, In an ellipse, 

Ends of the major axis (± 3, 0), ends of minor axis (0, ± 2)

Here, 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( ends of the major and minor axis ) with the given one, we get 

a=3 and b=2

Hence, The Equation of the ellipse will be :

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

Which is 

\frac{x^2}{9}+\frac{y^2}{4}=1.

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