A rod of length `l` slides with its ends on two perpendicular lines. Find the locus of its midpoint.

Explanation

`x=2α`

`y=2β`

`x^2+y^2=1^2`

`(2α)^2+(2β)^2=1^2`

`α^2+β^2=frac{1^2}{4}`

`frac{x^2}{4}+frac{y^2}{4}=frac{1^2}{4}`

`x^2+y^2=l^2`