TS EAMCET 4 May 2018 Shift 1 Solved Paper

Consider the equation of ellipse.

x2

a2

+

y2

b2

=1
The equation of tangent on the ellipse is,
frac‌xx1‌a2+frac‌yy1‌b2=1The intersecting point of tangent with the axes is,
A(

a2

x1

,0) and B(0,

b2

y1

)
Let the middle point of point A and B is P(h,k)
h=

a2

2x1

And,
k=

b2

2y1

Therefore,
x1=

a2

2h

And,
y1=

b2

2k

The points (x1,y1) lie on the ellipse.
Thus,

a2

h2

+

b2

k2

=4
Take locus of the point (h,k)

a2

x2

+

b2

y2

=4