Find the equation of the ellipse having centre at 1 2 one focus at 6 2 and passing through the point...........

Mathematics (NDA) Coordinate Geometry

Find the equation of the ellipse having centre at (1, 2), one focus at (6, 2), and passing through the point (4, 6).?

x²/ 45 +y²/16 =1

x²/ 42 +y²/20 =1

x²/ 35 +y²/20 =1

x²/ 45 +y²/20 =1

centre at (1, 2)

focus at (6, 2)

equation of ellipse with centre (1,2)

(x-1)²/a² +(y-2)² /b²

Passing through point (4,6)

9/a² +16/b²=1 ……….1

distance between centre to focus ae=6-1=5

b²=a²(1-e²)

b²=a²-25 equation ….2

solving 1 and 2

a²=45 ,b²=20

x²/ 45 +y²/20 =1

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