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 ?
The radius can be found by finding the distance from the centre to any of the axes.
Correct, let us find the distance from the centre to the x-axis first. Since the circle touches the x-axis, its distance from the centre will be equal to the radius, r. So, the distance from (a,b) to the x-axis is |b|. Hence, the equation of the circle can be written as (x-a)^2 + (y-b)^2 = b^2. Can you substitute a = 2b+3 in this equation and simplify it?