Which circles lie completely within the fourth quadrant?

A circle with centre (x0, y0) and radius r has the equation of:

(x -x0)² + (y - y0)² = r²

By writing the equation of any circle in this form its centre and radius can be determined.

To completely lie within a quadrant, the centre of the circle must be more than r away from the y- and x-axes:

• In the first quadrant if: x0 > r and y0 > r
• In the second quadrant if: x0 < -r and y0 > r
• In the third quadrant if: x0 < -r and y0 < -r
• In the fourth quadrant if: x0 > r and y0 < -r

If either x0 or y0 (or both) is exactly r away from the y- or x-axis then the circle is on boundary between quadrants, and if either x0 or y0 (or both) is less than r away from the y- or x-axis, then the circle is in more than one boundary.

f x0 < r from the y-axis then the circle is in quadrants I and II, or y0 < r from the x-axis then the circle is in quadrants III and IV; if both less than r away from their respective axes, the the circle is in all four quadrants.