Let O be the center and let F be one of the foci of the ellipse 25x^2 +16 y^2 = 400. A second ellipse, lying inside and tangent to the first ellipse, has its foci at O and F. Where is the center of the second ellipse?
+128408 25x^2 + 16y^2 = 400 divide through by 400
x^2 y^2
____ + ____ = 1
16 25
The center is (0,0)........the foci lies on the y axis .....so let F = (0, sqrt (25 - 16) = (0, sqrt (9) ) =
(0, 3 ) = F
The center of the second ellipse is the the midpoint of O and F = (0,0) and (0,3) = (0, 3/2)
