What is the area of the circle x^2 + y^2 - 6x +12 y= 20?

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The equation of the circle given is x^2 + y^2 - 6x +12y= 20

x^2 + y^2 - 6x +12y= 20

=> x^2 - 6x + 9 + y^2 + 12y + 36 = 20 + 9 + 36

=> (x - 3)^2 + (y + 6)^2 = (sqrt 65)^2

The radius of the circle is sqrt 65

The area of the circle is pi*r^2 = pi*65

The area of the circle is 65*pi

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

Posted on

Given the equation of the circle :

x^2 + y^2 - 6x + 12y = 20

First we will rewrite the equation into the standard form

(x-a)^2 + (y-b)^2 = r^2 such that r is the radius.

We will complete the square for x^2 -6x and y^2 +12y

==> x^2 - 6x + 9 -9 + y^2 + 12y +36 - 36 = 20

==> (x-3)^2 + (y+6)^2 = 20 + 9 + 36

==> (x-3)^2 + (y+6)^2 = 65

Then the radius of the circle is sqrt65.

Now we will calculate the area.

==> A = r^2 * pi = sqrt65^2 * pi 65pi

Then the area of the circle is 65pi square units.

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