Question

Find the equation for the ellipse that satisfies the given conditions: Ends of major axis $(±3,0)$ ends of the minor axis $(0,±2)$

Answer 1

Given that , the ends of the major axis $( ±3, 0)$, ends of minor axis $(0, ±2)$ $$
Here, the major axis is along 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, $a = 3$ and $b = 2.$
Thus, the equation of the ellipse is $\dfrac{x^2}{3^2} \+ \dfrac{y^2}{2^2} = 1$ or $\dfrac{x^2}{9} \+ \dfrac{y^2}{4} = 1$. (Ans)