Question

17.Foci (± 3、0), a = 4

Answer 1

The given foci of ellipse are ( ±3,0 ) and a=4 , where a is the length of the semi-major axis.

Since the foci are on the x axis, 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 (2)

Substitute the values of c and a in equation (2)

3= 4 2 − b 2 3 2 =16− b 2 b 2 =16−9 b= 7

Substitute the values of a and b in equation (1)

x 2 4 2 + y 2 7 2 =1 x 2 16 + y 2 7 =1

Therefore, the equation of the ellipse with foci ( ±3,0 ) and a=4 is x 2 16 + y 2 7 =1 .