Find the equation for the ellipse that satisfies the given conditions
$b = 3$ , $c = 4$ , centre at the origin foci on $x - a x i s$

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Solution

Given: Length of minor axis $b = 3$ and distance between centre and either foci $c = 4$
Equation of ellipse centred at origin with its foci on x-axis: $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$

$∵ c^{2} = a^{2} = b^{2} ∴ 4^{2} = a^{2} - 3^{2} \Rightarrow 19 + 9 = a^{2} \Rightarrow a^{2} = 25$

Thus, the equation of ellipse is $\frac{x^{2}}{25} + \frac{y^{2}}{9} = 1$

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