Question

Given an equation of circle(x-2)2+(y-3)2=25,find the equation of the image circle after a reflection about the line y=x+3

Answer 1

the reflection is along a line through the center of the circle, perpendicular to the given line

slope of perpendicular is ... -1

equation of perpendicular
... y-3 = -1 (x-2) ... y = -x + 5

intersection with reflecting line
... (1,4)

center of reflected circle
... (0,5)

center has moved, but radius is the same