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

1 Answer
Sep 10, 2017

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#