TS EAMCET 11-Sep-2020 Shift 2 Solved Paper

Given ellipse
2x2+y2=2 or x2+‌

y2

2

=1
Here, ‌‌a2=1,b2=2
Equation of tangent
x+2y+k=0 or 2y=−x−k
or ‌‌y=−‌

x

2

−‌

k

2

Here, ‌‌c=‌

−k

2

,m=−‌

1

2

From the condition of tangent
‌

−k

2

=±√‌

9

4

⇒‌

−k

2

=±‌

3

2

or k=±3
But k>0, so, k=3
So, equation of tangent, y=−‌

x

2

−‌

3

2

and point is (‌

1

√2

,1)
The equation of the normal to the ellipse at point (x1,y1) is given by
√2x−2y=−1 or √2x−2y+1=0