# Find the equation for the ellipse that satisfies the given conditions: Foci (±3, 0), a = 4

Question:

Find the equation for the ellipse that satisfies the given conditions: Foci (±3, 0), a = 4

Solution:

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 $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$, where $a$ is the semi-major axis.

Accordingly, c = 3 and a = 4.

It is known that $a^{2}=b^{2}+c^{2}$.

$\therefore 4^{2}=b^{2}+3^{2}$

$\Rightarrow 16=b^{2}+9$

$\Rightarrow b^{2}=16-9=7$

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