Find the Langitude and Longitude of the centre point of a circle given a point on the circumference.

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I couldn't find a similar question!

Given I have the latitude and longitude (x,y) of a point on the circumference of a circle, and I want the circumference to be 1000m. An example of a lat lang I have is

lat="52.4245085" lon="-1.9441316"

(please correct the below if wrong) I got

diameter = 1000/pi
radius = diameter/2

How do I find the lang and lat of the centre point on my circle? I would like this point to be a plottable point on the earths surface. I am aware I probably need to use the radius of the earth if I am to scale this which is 6 378.1km.

Would really appreciate any help or guidance on this.

As you can probably tell my maths knowledge isn't great, so if you could try and keep your answers simple I would be very really thankful.

edit: I understand that there are many possible solutions. I am trying to find just one circle, I understand there is not simply one unique one. If I also have a bearing (b) does this make a solution possible? The circle should run flat on the earth.