The conversation between human and AI assistant.
Find the equation of a circle which touches the coordinate axes and whose centre lies on a line x-2y=3 ?
Can you help me find the equation of a circle that touches the coordinate axes and whose centre lies on a line x-2y=3?
Sure, let me help you with that. The equation of a circle with centre (a,b) and radius r is given by (x-a)^2 + (y-b)^2 = r^2. Now, we have been given that the circle touches the x-axis and the y-axis, which means that the centre lies on a line passing through the origin and is perpendicular to both the x and y-axes. Can you tell me the equation of this line?