Question

Find the equation for the ellipse that satisfies the given conditions: Foci $(±3,0),$ $a=5$

Answer 1

Gven that, foci $( ±3, 0)$, $a= 4$
Since the foci are on the $x-axis$, the major axis is along the $x-axis$
Therefore, the equation of the ellipse will be of the form $\dfrac{x^2}{a^2} +\dfrac{ y^2}{b^2} = 1$, where $a$ is the semi-major axis.
Accordingly, $c = 3$ and $a = 4$.
It is known that

$a^2 = b^2 \+ c^2$

$∴ 4^2 = b^2 \+ 3^2$

$⇒ 16 = b^2 \+ 9$

$⇒ b^2 = 16 – 9$

$⇒ b^2 = 7$

Thus, the equation of the ellipse is $\dfrac{x^2}{16} + \dfrac{y^2}{7} = 1$