Solving a equation of a circle

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SUMMARY

The discussion focuses on solving the equation of a circle given by x² + y² + 2√2x - 4√5y = 5. To find the center and radius, the equation must be transformed into the standard form (x-h)² + (y-k)² = r². The key steps involve grouping the terms and completing the square for both x and y variables. This method allows for the identification of the center (h, k) and the radius r of the circle.

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  • Understanding of completing the square in algebra
  • Familiarity with the standard form of a circle's equation
  • Basic knowledge of quadratic equations
  • Ability to manipulate algebraic expressions
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  • Learn how to complete the square for quadratic equations
  • Study the derivation of the standard form of a circle's equation
  • Explore examples of converting general quadratic equations into standard form
  • Practice solving equations of conic sections
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Students studying algebra, mathematics educators, and anyone interested in understanding the geometric properties of circles through their equations.

mrpk
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Find the center and radius of the circle using the equation:

x^2 + y^2 + 2√2x - 4√5y = 5

I just can't seem to solve this equation into the form (x-h)^2 + (y-k)^2 = r^2 in order to get the center and radius.

Any help would be appreciated
 
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You would need to show us what you have tried. First thing you do is group up the terms and complete the square.
 

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