TS EAMCET 6-Aug-2021 Shift 1 Question Paper

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).