Locus Help :'( (1 Viewer)

[Soulful]

Could someone help me with this locus question?

"Find the equation of the locus of the midpoints of all chords of length 4 units of the circle with the equation x^2+y^2-4x+2y=4

I'm just completely lost about how to tackle this question (I only heard something called loci existed like, 12 hours ago). Am I missing something really obvious? Please help :'(

 

[Drongoski]

For 2U Maths, how to do this question is not immediately obvious.

If I'm not mistaken, the required locus is the circle, centre (2, -1) and radius sqrt(5).

i.e. (x-2)^2 + (y+1)^2 = 5

i.e. x^2 + y^2 -4x +2y = 0

 

[Soulful]

For 2U Maths, how to do this question is not immediately obvious.

If I'm not mistaken, the required locus is the circle, centre (2, -1) and radius sqrt(5).

i.e. (x-2)^2 + (y+1)^2 = 5

i.e. x^2 + y^2 -4x +2y = 0

Could you give a hint about how to get there? :3

Edit: Is it something to do with perpendicular distance?
Edit2: I think I got it... note to self: don't do maths questions after 11

 

[Drongoski]

It would be useful for you to show your fully worked out solution - so you know your reasonings are right.