Find the equation in the standard form of the ellipse with f

Find the equation, in the standard form, of the ellipse with foci at (4, 0) and (4, -6) whose major axis has the length of 10. Graph the ellipse.

Solution

This is an ellipse with vertical major axis.
Its standard form of equation:

[(x-h)^2/a^2 + (y-k)^2/b^2]=1, a>b,

(h,k)=(x,y) coordinates of center

For given ellipse:
center: (4,-3)
given length of vertical major axis=10=2a
a=5
a^2=25
c=3(distance from center to foci)    that is (4,-3) and (4,0) you will get distance =3

c^2=9
c^2=a^2-b^2
b^2=a^2-c^2=25-9=16                , therefore b=4    
Equation of given ellipse:     [(x-4)^2/16 + (y+3)^2/25 ]=1