find the equation of the circle whose centre lies on the line 5x-2y=9 and the circle touches both the positive axes

Answer 1

The center has to be on the line
y = x
if the circle is tangent to the x and y
axes.

so center on 3 x = 3 y = 9
or
(3,3)
and the radius is 3
so
(x-3)^2 + (y-3)^2 = 9