Find the center and the radius of the circle x^2+y^2 -8x+14y= 12

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justaguide | College Teacher | (Level 2) Distinguished Educator

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We can write the given equation of the circle x^2 + y^2 - 8x +14y = 12 in the form (x - a)^2 + (y - b)^2 = r^2 where the center of the circle is (a, b) and r is the radius.

x^2 + y^2 - 8x +14y = 12

=> x^2 - 8x + 16 + y^2 + 14y + 49 = 12 + 49 +16

=> (x - 4)^2 + (y + 7)^2 = (sqrt 77)^2

The center of the circle is (4 , -7) and the radius is sqrt 77.

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hala718 | High School Teacher | (Level 1) Educator Emeritus

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We have the equation of the circle :

x^2 + y^2 - 8x +14y = 12

We will rewrite into the standard form: ( x-a)^2 + (y-b)^2 = r^2 such that (a,b) is the center and r is the radius.

==> We will rewrite by completing the square.

==> x^2 - 8x + 16 -16 + y^2 + 14y + 49 - 49 = 12

==> (x-4)^2 + (y+7)^2 = 12 + 49 + 16.

==> (x-4)^2 + (y+7)^2 = 77

Then the center of the circle is (4,-7) and the radius is sqrt77.

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