What is the minimum distance of the circle given by the equation x² − 10x + y² + 12y + 57 = 0 from the coordinate axes?
A) 3
B) 2
C) 4
D) 5
E) 1
IMAT 2023 · Question 54
Q54 - Circle and circumference
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The correct answer is A) 3.
Complete the square: (x − 5)² + (y + 6)² = 25 + 36 − 57 = 4. So the centre is (5, −6) and the radius is 2.
The centre is 5 from the y-axis and 6 from the x-axis. Taking off the radius, the circle gets within 3 of the y-axis and 4 of the x-axis.
The minimum distance is 3.
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