Find the standard form the equation of the ellipse satisfyin

Find the standard form the equation of the ellipse satisfying the given conditions. Endpoint of major axis: (6, 12) and (6, 0) Endpoints of minor axis: (11, 6) and (1, 6) Standard form of the equation:

Solution

Solution:

Here;

length of major axis:

l(major) =(6-6)² +(12-0)² = 12 = 2a

=> a = 6

and

length of minor axis:

l(minor) = 10 = 2b

=> b = 5

Mid point of major axis:

(h,k) = ((6+6)/2 , 12+0 /2)

=> (h,k) = (6,6)

Hence the standard form of ellipse is:

(x-h)²/a² + (y-k)²/b² = 1

=> (x-6)²/6² + (y-6)²/5² = 1