A stick of length `l` slides with its ends on two mutually perpendicular lines. Find the locus of the middle point of the stick.

Explanation

Let the stick intercepts x-axis at point `(a,0)` and y-axis at point `(0,b)`

and `(alpha, beta)` are midpoints of the stick. then,

`(a+0)/2 = alpha => a = 2alpha`

`(b+0)/2 = beta=> b= 2beta`

Then, `l^2 = (a-0)^2+(0-b)^2`

Here, `l` is the length of stick.

`=>l^2 = a^2+b^2 `

`=>l^2 = (2alpha)^2+(2beta)^2`

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