Question

15.Length of major axis 26, foci (+ 5, 0)

Answer 1

The given length of the major axis is 26 and foci is (±5,0)

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 axis is the major axis.(1)

Length of the major axis = 2a

So, 2a=26 a=13

Foci of ellipse are represented as (±c,0)

Hence, c=5

Also,

c 2 = a 2 − b 2 5 2 = 13 2 − b 2 b 2 =169−25 b 2 =144 b=12

By substituting a and b in equation (1), we get

x 2 13 2 + y 2 12 2 =1

Thus, the equation of ellipse with foci ( ±5,0 ) and length of major axis as 26 is x 2 169 + y 2 144 =1 .