TS EAMCET 10-Sep-2020 Shift 2 Solved Paper

Equation of ellipse ‌

x2

a2

+‌

y2

b2

=1
e=‌

2√2

3

Length of major axis is the diameter of circle
x2+y2=18\∴‌‌2a=2(3√2)2⇒a=3√2
e2=1−‌

b2

a2

⇒‌‌‌

8

9

=1−‌

b2

18

⇒b2=2
∴ Equation of ellipse is ‌

x2

18

+‌

y2

2

=1
Equation of circle is x2+y2=18
Let (h,k) be the pole, then equation of polar with respect to ellipse is
‌

xh

18

+‌

yk

2

=1
Since this is the tangent of circle
∴ 3√2=∣‌

1

√‌ h2 (18)2 +‌ k2 4

‌

h2

182

+‌

k2

4

‌‌=‌

1

18

‌

h2

18

+‌

9k2

2

‌‌=1
∴ Locus is ‌

x2

18

+‌

9y2

2

=1