MHB Find Center and Radius of Circle

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To find the center and radius of the circle represented by the equation x^2 + y^2 - 10x + 2y + 17 = 0, completing the square is an effective method. The equation can be rearranged into the form (x^2 - 10x + ?) + (y^2 + 2y + ?) = ?. By selecting appropriate values to complete the squares, the center and radius can be easily determined. This approach confirms that the circle's properties can be extracted directly from the transformed equation. Completing the square is a reliable technique for solving such problems.
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Determine the center and the radius of circle.

x^2 + y^2 - 10x + 2y + 17 = 0

Can this be done using completing the square?
 
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RTCNTC said:
Determine the center and the radius of circle.

x^2 + y^2 - 10x + 2y + 17 = 0

Can this be done using completing the square?
Yes! Write the equation in the form $(x^2 - 10x +\ ?) + (y^2 + 2y +\ ?) =\ ?$ (choosing the queries so as to complete the squares), and you should be able to read off the answer.
 
Opalg said:
Yes! Write the equation in the form $(x^2 - 10x +\ ?) + (y^2 + 2y +\ ?) =\ ?$ (choosing the queries so as to complete the squares), and you should be able to read off the answer.

I got it.
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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