Find the equation of the ellipse whose foci are 2 3 ndash 2 3 and whose semi minor axis is of length...........

Mathematics (NDA) Coordinate Geometry

Find the equation of the ellipse whose foci are (2, 3), (–2, 3), and whose semi-minor axis is of length √5?

x²/9 +(y)²/5 =1

x²/3 +(y-3)²/5 =1

x²/9 +(y-3)²/5 =1

x²/4 +(y-3)²/5 =1

Here S is (2, 3) & S' is (–2, 3) and b =√5

SS' = 4 = 2ae

ae=2

b²= a² (1 – e² )

5 = a²-4

a²=9

a=3

centre is mid point of ss^’ =2+(-2) /2 ,3+3/2

=0,3

Equation of ellipse x²/9 +(y-3)²/5 =1

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