posted by Melba .
standard equations of circles that have centers on line 5x-2y=-21 and are tangent to both axis.
First express the line as in point slope form
y=(5/2)x - 21/2
The center must be on the line, so it is a point expressed as
(x,(5/2)x - 21/2)
In order for the circle to be tangent to both axis the center must be the same distance from both axis, so
x=y or x=(5/2)x - 21/2 solve for x
The standard equation for the circle is
You should be able to determine a,b and r.
After review, I don't know if I suggested how to find all the solutions.
You need to look at |x|=|y| or
|x|=|5/2)x - 21/2|
There should be one more solution to the question.
Thanks for all your help...