Find the standard form of the equation of the ellipse satisf

Find the standard form of the equation of the ellipse satisfying the given conditions. Endpoints of major axis: (4.8) and (4.0) Endpoints of minor axis: (6.4) and (2,4) Standard form of the equation:

Solution

end points of major axis : (4,8) and (4,0)

2a = 8-0 = 8 ----> a =4

end points of minor axis: (6,4) and (2,4)

2b = 6-2 =4 ----> b = 2

The major and minor axis intersect at ( 4, 4) centre

So, equation ellipse : (x-h)^2/a^2 + (y-k)^2/b^2 =1

(x-4)^2/16 + (y -4)^2/4 =1