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)

Answers (1)

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 bare 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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