Doubt on locus of a median point

Question

I'm learning about geometric locus and ain't had an good time, I'm struggling with this problem:

By the way, any study resource on geometric locus is welcome!

Given an segment $AB$ formed by points $A(a, 0)$ and $B(0, b)$ with a constant length of $2l$. Determine the equation for the locus the median point $P$ of $AB$.

Facts I know:

The median point M can the seen as $M(\dfrac{a}{2}, \dfrac{b}{2})$. How to proceed to find this equation ?

Answer 1

The question possibly creates confusion by using $a$ and $b$, which could be assumed to mean constants.

I am guessing the question is:

If segment $AB$ varies such that $A$ is on the $x$-axis, $B$ in on the $y$-axis, and the length of the segment is the constant $2l$, what is the equation of the locus of the midpoint of $AB$.

Now if $A$ was $(x,0)$ and $B$ was $(0,y)$, what is the relation between $x$ and $y$ which will ensure that the length of the segment $AB$ is $2l$?

Spoiler:

$x^2 + y^2 = 4l^2$

Using that, can you find an equation for the locus of the midpoint $(x', y')$?

Spoiler:

$x'^2 + y'^2 = l^2$