TS EAMCET 10-Sep-2020 Shift 2 Solved Paper

Since the foci of given ellipse lie on the Y -axis, it is vertical ellipse.
Let the required equation be ‌

x2

b2

+‌

y2

a2

=1
Where a2>b2
Foci are (0,±c)=(0,±1)⇒c=1
a= length of the semi-major axis =‌

1

2

×√5=‌

√5

2

∴ a2=‌

5

4

Now, ‌‌c2=a2−b2⇒1=(‌

√5

2

)2−b2
⇒‌‌b2=‌

5

4

−1=‌

1

4

∴ The required equation is
‌

x2

1∕4

+‌

y2

5∕4

=1⇒4x2+‌

4y2

5

=1
⇒‌‌20x2+4y2=5