# Find the equation of ellipse whose foci are (2, 3), (-2, 3) and whose semi major axis is of length $$\sqrt{5}$$.

## Solution :

Here S = (2, 3) & S’ is (-2, 3) and b = $$\sqrt{5}$$ $$\implies$$ SS’ = 4 = 2ae $$\implies$$ ae = 2

but $$b^2$$ = $$a^2(1-e^2)$$ $$\implies$$ 5 = $$a^2$$ – 4 $$\implies$$ a = 3

Hence the equation to major axis is y = 3.

Centre of ellipse is midpoint of SS’ i.e. (0, 3)

$$\therefore$$ Equation to ellipse is $$x^2\over a^2$$ + $${(y-3)}^2\over b^2$$ = 1 or $$x^2\over 9$$ + $${(y-3)}^2\over 5$$ = 1

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