Question

Find the equation for the ellipse that satisfies the given conditions: Ends of major axis(0,±√5) ends of minor axis ( ±1,0)

Answer 1

Given that, the ends of the major axis$(0, ±√5)$ , ends of minor axis $( ±1, 0)$
Here, the major axis is along the $y-axis.$
Therefore, the equation of the ellipse will be of the form $\dfrac{x^2}{b^2}+ \dfrac{y^2}{a^2} = 1$, where ‘a’ is the semi-major axis.

Accordingly, a = √5 and b = 1.

∴ The equation for the ellipse $\dfrac{x^2}{1^2}+ \dfrac{y^2}{(√5)^2} = 1$or $\dfrac{x^2}{1}+ \dfrac{y^2}{5} = 1$ (Ans)