Question 877552
find standard form of an ellipse giving foci:(3,3) , (-1,3); Major axis length of 6
***
given foci coordinates show ellipse has a horizontal major axis.
Its standard form of equation:{{{(x-h)^2/a^2+(y-k)^2/b^2=1}}}, a>b, (h,k)=coordinates of center
For given ellipse:
center: (1,3)
length of major axis=6=2a
a=3
a^2=9
c=2 (distance from center to foci)
c^2=4
c^2=a^2-b^2
b^2=a^2-3^2=9-4=5
equation:{{{(x-1)^2/9+(y-3)^2/5=1}}}