# Algebra

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find the center (h,k) and radius r of the circle with the given equation:

x^2 + y^2 + 6x - 8y = 56

• Algebra -

This can be done by completing the square, namely we group the x² with the 6x term and add a constant to make it a complete square. The same goes for y.
x²+6x+ y²-8y = 56
(x+3)² -9 + (y-4)² -16 = 56
(x+3)² + (y-4)² = 56 + 9 + 16 = 81 = 9²
Thus the equation of the circle is
(x+3)² + (y-4)² = 9²
meaning that the centre is at (-3,4) and the radius is 9.

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