Question

How do you find the equation of a circle radius 3 units and its center lies on the line y=x-1?

Answer 1

There are infinitely many such circles, but their equations can be expressed as:

`(x-a)^2+(y-a+1)^2=9`

for any real value of `a`.
See explanation.

Explanation:

The general equation of a circle with center in `C=(a,b)` and radius `r` is

`(x-a)^2+(y-b)^2=r^2` ##

In our task the radius is given (it is `3`), but the center is not defined. The only information we have is that it lies on `y=x-1`, so we can write the center as `C=(a,a-1)` for some real value of `a` which leads to:

`(x-a)^2+(y-a-1)^2=9`