1
$\begingroup$

As shown in the graph below, a circle touches the $x$-axis, the $y$-axis and a line that has equation $y = x/2 +2$.

How to find the equation of the circle?

enter image description here

Thanks very much!

  • 0
    Are you sure that's the line $y=\frac{x}{2}$?2012-11-13
  • 0
    If I'm reading this correctly, and $y = \frac{1}{2}x$, then the line must pass through the origin.2012-11-13
  • 0
    Oh sorry, I'll edit it2012-11-13
  • 0
    **Hint:** the center of the circle is equidistant from both axis and from the line.2012-11-13
  • 0
    yea, what should I do next?2012-11-13
  • 0
    You might start by writing down the equation of a circle which is tangent to both axes. This equation will have a special form. Then, figure out what the distance from an arbitrary point $(x_0,y_0)$ is to your line. This will help you decide what the radius needs to be. If you can't figure it out, I'll type up a solution (but give it another shot!)2012-11-13
  • 0
    Sorry, my torch just won't light, can you please show me the way?2012-11-13
  • 0
    A cavil about terminology: you’re looking not for a function, but for an equation.2012-11-13

4 Answers 4