What is the center and radius of a circle with equation y^2-4*y+x^2-8*x+4 =0

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The equation of a circle with center (a, b) and radius r is (x - a)^2 + (y - b)^2 = r^2.

The equation of the circle in the problem is y^2-4*y+x^2-8*x+4 =0. Let us rewrite this in the form given earlier so that the center and radius can be determined.

y^2-4*y+x^2-8*x+4 =0

=> y^2 - 4y + 4 + x^2 - 8x + 16 = -4 + 4 + 16

=> (y - 2)^2 + (x - 4)^2 = 16 = 4^2

The center of the given circle is (4, 2) and the radius of the circle is 4 units.

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