प्रतिबंधों को संतुष्ट करते हुए दीर्घवृत्त का समीकरण ज्ञात कीजिए

शीर्षों $(\pm 5,0),$ नाभियाँ $(±4,0)$

Vertices $(\pm 5,\,0),$ foci $(±4,\,0)$

Here, the vertices are on 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, $a=5$ and $c=4$

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

$\therefore 5^{2}=b^{2}+4^{2}$

$\Rightarrow 25=b^{2}+16$

$\Rightarrow b^{2}=25-16$

$\Rightarrow b=\sqrt{9}=3$

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