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# Find the equation of an ellipse that satisfies the following conditions: $b=3, c=4$, centre at origin and foci on x-axis.

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 length of major axis and foci, we know a and c, so we can calculate be and we can substitute in the above equation and arrive at the equation.
Given $b = 3$, $c = 4$, we can caclulate $a$
$c^2 = a^2 + b^2 \rightarrow 16 = a^2-9 \rightarrow b = \sqrt{25} = 5$
We therefore can write the equation of the ellipse as $\;\large\frac{x^2}{5^2}$$+\large\frac{y^2}{3^2}$$=1$
$\Rightarrow$ The equation of the ellipse is $\large\frac{x^2}{25}$$+\large\frac{y^2}{9}$$=1$
edited Apr 3, 2014