Question

A circle in quadrant II is tangent to both axes. It touches the y-axis at (0,3). a.At what point does it meet the x-axis? b. Find the coordinates of the center of the circle.

Answer 1

If an axis is at a tangent, it is right angles to the radius, so the y axis (x=0) is a distance of 3 units to the right of the centre, making the centre 3 units to the left at x=-3. Because the axis is also a tangent it must be above the x-axis by 3 units (y=3), so the centre is at (-3,3).