Question 877541
find an equation of the ellipse having foci (-1,0) and (7,0) and with 10 as the sum of the focal radii.
foci coordinates show ellipse has a horizontal major axis.
Its standard form of equation:{{{(x-h)^2/a^2+(y-k)^2/b^2}}}, a>b, (h,k)=coordinates of center
For given ellipse:
center: (3,0)
sum of the focal radii=10=length of major axis=2a
a=5
a^2=25
c=4
c^2=16
c^2=a^2-b^2
b^2=a^2-c^2=25-16=9
equation:{{{(x-3)^2/25+y^2/9}}}