It is given that c=4 , b=3 ,center is at the origin and foci are on the x axis.
Since the foci are on the x axis, so the equation of the ellipse is represented as x 2 a 2 + y 2 b 2 =1 , where x is the major axis.(1)
The relationship between the semi-major and semi-minor axes and the distance of the focus from the center of the ellipse is represented as:
c= a 2 − b 2
4= a 2 − 3 2 4 2 = a 2 − 3 2 a 2 =16+9 a=±5
Substitute the values of a and b in equation (1)
x 2 5 2 + y 2 3 2 =1 x 2 25 + y 2 9 =1
Therefore, the equation of the ellipse with c=4 , b=3 , center at origin and foci at x axis is x 2 25 + y 2 9 =1 .