# Find the equation of the ellipse whose axes are along the coordinate axes, vertices are $$(0, \pm 10)$$ and eccentricity e = 4/5.

## Solution :

Let the equation of the required ellipse be

$$x^2\over a^2$$ + $$y^2\over b^2$$ = 1                 ……….(i)

Since the vertices of the ellipse are on y-axis.

So, the coordinates of the vertices are $$(0, \pm b)$$.

$$\therefore$$    b = 10

Now, $$a^2$$ = $$b^2(1 – e^2)$$  $$\implies$$  $$a^2$$ = 100(1 – 16/25) = 36

Substituting the values of $$a^2$$ and $$b^2$$ in (i), we obtain

$$x^2\over 36$$ + $$y^2\over 100$$ = 1  as the required equation of the ellipse.

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