Question

A Rod of length "l" units slides with one end of its end on x-axis and other on y=x. Find locus of its mid point.​

Answer 1

Let (h,k) be the mid point of the line. Also let (a,0) and (0,b)$$ be the end points of the line.

Then by the problem,

a

2

+b

2

=l

2

......(1).

Now the mid point of the line be (

2

a

,

2

b

).

Then

2

a

=h and

2

b

=k

or, a=2h and b=2k.

Putting this values of a,b in (1) we get,

4(h

2

+k

2

)=l

2

or, h

2

+k

2

=

4

l

2

.

So locus of (h,k) is x

2

+y

2

=

4

l

2

.