Ellipse

Given, ellipse is x2+2y2=2
or ‌

x2

2

+y2=1
Now, equation of tangent in parametric form is
‌

x

√2

‌cos‌θ+ysin‌θ=1
Now, coordinate of X-intercept
=(√2 secθ,0)A
Coordinate of Y-intercept
=(0,cosec‌θ)B
Let P(h,k) be the points which is the mid-points of A and B.
h‌=‌

√2 secθ

2

‌ and ‌k=‌

cosec‌θ

2

secθ‌=√2h‌ and ‌cosec‌θ=2k
cos‌θ‌=‌

1

√2h

‌ and ‌sin‌θ=‌

1

2k

Using sin‌2θ+cos2θ=1
‌

1

2h2

+‌

1

4k2

=1
Taking locus of P(h,k), we get
‌

1

2x2

+‌

1

4y2

=1