TS EAMCET 14-Sep-2020 Shift 2 Solved Paper

Given ellipse,
x2+2y2=2⇒‌

x2

2

+‌

y2

1

=1
Point P(√2‌cos‌θ,sin‌θ) lie in ellipse
Tangent at P(√2‌cos‌θ,sin‌θ) on ellipse is,
x‌cos+√2‌sin‌θ‌y=√2
Intercept on line is, A(‌

√2

cos‌θ

,0) andB(0,‌

1

sin‌θ

)
Let (h,k) is mid-point of the AB.
∴h=‌

√2

2‌cos‌θ

‌ and ‌k=‌

1

2‌sin‌θ

⇒cos‌θ=‌

1

√2h

‌ and ‌sin‌θ=‌

1

2k

Squaring and adding, we get
‌

1

2h2

+‌

1

4k2

=1
∴ Locus is, ‌

1

2x2

+‌

1

4y2

=1