Geometry and TrigonometryHardCentre of a circle from its general-form equation
Geometry and Trigonometry practice question
In the xy-plane, the equation x² + y² − 6x + 4y − 12 = 0 represents a circle. What is the sum of the x- and y-coordinates of the circle's centre?
Answer: 1
Complete the squares: (x − 3)² + (y + 2)² = 12 + 9 + 4 = 25. The centre is (3, −2), and 3 + (−2) = 1.
Common wrong answers
- If you answered 5
- 5 is the radius.
- If you answered -1
- −1 comes from a centre of (−3, 2), reading the signs the wrong way.
- If you answered -2
- −2 is the y-coordinate of the centre alone.
More Geometry and Trigonometry questions
- Hard
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A circle is defined by the equation (x − 3)² + (y + 2)² = 25. What is the radius of the circle? - Hard
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What is the length of segment PT? - Hard
What is the measure, in degrees, of the central angle of this sector?
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