AMU Engineering 2018 solved paper Solved Paper

Let A and B are the extremities on two fixed straight line of the given line.
∴ Coordinates of A(a,0) and B(0,b)
Let (h,k) is the mid-point of AB.
∴h=

a

2

and k=

b

2

Now, area of ΔOAB=

1

2

ab=c2
On putting the value of a and b, we get

1

2

(2h)(2k)=c2⇒2hk=c2
∴ Locus of the mid-point of the line is 2xy=C2