SAT Math: Circles Tangent to the X or Y Axes
18+ practice questions in Praczo
The concept, explained
- 1
A circle is tangent to a line if it touches the line at exactly one point.
- 2
If a circle is tangent to the x-axis, its radius "r" is exactly equal to the absolute value of the y-coordinate of its center |k|.
- 3
If a circle is tangent to the y-axis, its radius "r" is equal to the absolute value of the x-coordinate of its center |h|.
- 4
If tangent to both axes, the center must be at (r, r), (-r, r), (-r, -r), or (r, -r).
- 5
Use this relationship to determine the radius when given the center, or vice versa.
- ✗ Swapping the relationships: using the x-coordinate for x-axis tangency instead of the y-coordinate.
- ✗ Forgetting to take the absolute value when the center has negative coordinates.
SAT-style practice
A circle in the xy-plane has its center at (5, -7) and is tangent to the y-axis. What is the radius of the circle?
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