Question

Find the equation for the ellipse that satisfies the given conditions:Vertices (±6,0),foci (±4,0)

Answer 1

Vertices $( ±6, 0),$ 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 = 6$$$ , c= 4. $
It is known that

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

$6^2 = b^2+4^2$

$36 = b^2 \+ 16$

$b^2 = 36 – 16$

$b = √20$$$

∴ The equation of the ellipse is $\dfrac{x^2}{6^2} + \dfrac{y^2}{(√20)^2} = 1$ or $\dfrac{x^2}{36} + \dfrac{y^2}{20} = 1$