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  4. The ellipse E1:(x2/9)+(y2/4)=1 is inscribed in a rectangle R whose sides are parallel to the coordinate axes. Another ellipse E2 passing through the point (0 , 4) circumscribes the rectangle R . The length (in units) of the major axis of ellipse E2 is

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Q. The ellipse $E_{1}:\frac{x^{2}}{9}+\frac{y^{2}}{4}=1$ is inscribed in a rectangle $R$ whose sides are parallel to the coordinate axes. Another ellipse $E_{2}$ passing through the point $\left(0 , 4\right)$ circumscribes the rectangle $R$ . The length (in units) of the major axis of ellipse $E_{2}$ is

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Solution:

Let the ellipse be $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$
Solution
As it is passing through $\left(0 , 4\right)$ and $\left(3 , 2\right)$ . So, $b^{2}=16$ and $\frac{9}{a^{2}}+\frac{4}{16}=1$ or $a^{2}=12$
So, the length of major axis $=2b=8$