AP EAMCET Engineering 2018 Apr 23 Shift 2 Paper

Let point A(a,0) and B(0,b) so equation of variable line is,

x

a

+

y

b

=1 .... (I)
Since the equation (I) passes through point (α,β) so,

α

a

+

β

b

=1 .....(II)
Now the centroid of triangle OAB is (

a

3

,

b

3

)=(h,k)
So,
a=3h‌and‌b=3k .....(III)
From equation (II) and (III),

α

3h

+

β

3k

=1
On taking locus of point (h,k) we get,
βx+αy−3xy=0