5x 2 + 9y 2 – 54y + 36 = 0

Sol. Let S and S' be the foci of ellipse

Let S ≡ (2, 3) and S ≡ (–2, 3)

Let C be the centre of the ellipse, then C ≡ (0, 3)

According to question semi minor axis b =

Also SS ′ = 4 ⇒ 2ae = 4 ⇒ ae = 2

Now b 2 = a 2 (1 – e 2 ) ⇒ 5 = a 2 – a 2 e 2 = a 2 – 4 ⇒ a = 3

Slope of SS ′ = 0, therefore major axis of the ellipse is parallel to x-axis and minor axis is parallel to y-axis.

Now equation of the required ellipse will be = 1

or 5x 2 + 9(y – 3) 2 = 45 or 5x 2 + 9y 2 – 54y + 36 = 0

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