# Find the equation for the ellipse that satisfies the given conditions:

Question:

Find the equation for the ellipse that satisfies the given conditions: b = 3, c = 4, centre at the origin; foci on the axis.

Solution:

It is given that b = 3, c = 4, centre at the origin; foci on the axis.

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, $b=3, c=4$.

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

$\therefore a^{2}=3^{2}+4^{2}=9+16=25$

$\Rightarrow a=5$

Thus, the equation of the ellipse is $\frac{x^{2}}{5^{2}}+\frac{y^{2}}{3^{2}}=1$ or $\frac{x^{2}}{25}+\frac{y^{2}}{9}=1$.