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# Find the equation of an ellipse that satisfies the following conditions: Major axis on x-axis, passes through the points $(4,3)$ and $(6.2)$

Toolbox:
• Given an ellipse as follows:
• http://clay6.com/mpaimg/Toolbar_7.png
• The equation of the ellipse is $\large\frac{x^2}{a^2}$$+\large\frac{y^2}{b^2}$$=1$
• $c= \sqrt {a^2 - b^2}$
• Given the two points the ellipse passes through, we can substitute in the equation to solve for $a^2$ and $b^2$
Given that the ellipse passes through the points $(4,3)$ and $(6.2)$
We therefore can write the equation of the ellipse as $\;\large\frac{16}{a^2}$$+\large\frac{9}{y^2}$$=1$ and $\;\large\frac{36}{a^2}$$+\large\frac{4}{y^2}$$=1$
Solving the above equations, we get $a^2 = 52, \; b^2 = 13$.
$\Rightarrow$ The equation of the ellipse is $\large\frac{x^2}{52}$$+\large\frac{y^2}{13}$$=1$