# 14. Find the equation for the ellipse that satisfies the given conditions:      Ends of major axis (0, ± $\sqrt{5}$ ), ends of minor axis (± 1, 0)

Given, In an ellipse,

Ends of the major axis (0, ±$\sqrt{5}$ ), ends of minor axis (± 1, 0)

Here, the major axis of this ellipse will be Y-axis.

Therefore, the equation of the ellipse will be of the form:

$\frac{x^2}{b^2}+\frac{y^2}{a^2}=1$

Where $a$ and $b$are the length of the semimajor axis and semiminor axis respectively.

So on comparing standard parameters( ends of the major and minor axis ) with the given one, we get

$a=\sqrt{5}$ and $b=1$

Hence, The Equation of the ellipse will be :

$\frac{x^2}{1^2}+\frac{y^2}{(\sqrt{5})^2}=1$

Which is

$\frac{x^2}{1}+\frac{y^2}{5}=1$.

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