Geometry and TrigonometryVery hardConstant in a circle's equation from a tangent line
Geometry and Trigonometry practice question
In the xy-plane, a circle with centre (2, −1) is tangent to the line y = 3. The equation of the circle is (x − 2)² + (y + 1)² = k. What is the value of k?
Answer: 16
The radius is the vertical distance from the centre to y = 3, which is 3 − (−1) = 4, so k = r² = 16.
Common wrong answers
- If you answered 2
- 2 uses the horizontal coordinate of the centre.
- If you answered 4
- 4 is the radius, not r².
- If you answered 9
- 9 uses radius 3, the line's y-value.
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