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 'Erroneously finding discrepancy in transpose rule'

Thread 'Erroneously finding discrepancy in transpose rule'

Obviously, there is something elementary I am missing here. To form the transpose of a matrix, one exchanges rows and columns, so the transpose of a scalar, considered as (or isomorphic to) a one-entry matrix, should stay the same, including if the scalar is a complex number. On the other hand, in the isomorphism between the complex plane and the real plane, a complex number a+bi corresponds to a matrix in the real plane; taking the transpose we get which then corresponds to a-bi...
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