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> Find the equation of the circle(s) touching the x-axis at a distance 3 from the origin and having an intercept of length $2\sqrt7$ on the y-axis, is...
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**I want specifically a geometrical method of solving this question.**

This is what I did:

[![enter image description here](https://i.stack.imgur.com/eSq3i.png)](https://i.stack.imgur.com/eSq3i.png)

As you can see, from the diagram that I have assumed that the centre is $(3,y\_1)$.
For the points, the circle intercepts the y-axis, x=0.

So the questions that want answers for are:  

1. Is the assumption I have made correct? *(Just a bit unsure about it.)*
2. How do I find the value of $y\_1$?
3. How to find the length of the radius?