Find the equation for the ellipse that satisfies the given conditions,
$b = 3, c = 4,$ centre at origin; foci on the x - axis.

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Solution

The foci lie on x - axis.
So the equation of ellipse in standard form is,
$\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$
We know that $c^{2} = a^{2} - b^{2}$
$∴ (4)^{2} = a^{2} - (3)^{2} \Rightarrow a^{2} = 16 + 9 = 15$
Thus equation of required elliipse is,
$\frac{y^{2}}{25} + \frac{y^{2}}{9} = 1.$

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