The foci are (−2,0) and (8,0). The distance between the foci is 2ae=10 ⇒ae=5 ∵e=
1
√2
(given) ∴a=5√2 Now, b2=a2(1−e2) ⇒b2=50(1−
1
2
)=25 ⇒b=5 The centre of the ellipse is the mid-point of the line joining two foci. Therefore, the coordinates of the centre is (3,0). Hence, its equation is
(x−3)2
50
+
(y−0)2
25
=1...(i) Thus, the parametric coordinates of a point on Eq. (i) are (3+5√2cosθ,5sinθ).