Question

Find the equation for the ellipse that satisfies the given conditions: Vertices $(±5,0),$foci (±4,0)

Answer 1

Vertices$( ±5, 0)$, foci $( ±4, 0)$
Here, the vertices are on 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, $a = 5$ and c = 4.
It is known that,

$a2 = b2 \+ c2.$

So, $5^2 = b^2 \+ 4^2$

$25 = b^2 \+ 16$

$b^2 = 25 – 16$

$b = √9$

$= 3$

∴ The equation of the ellipse is $\dfrac{x^2}{5^2} \+ \dfrac{y^2}{3^2} = 1$

$\dfrac{ x^2}{25} + \dfrac{y^2}{9} = 1$ (Ans)