Calculate the area of the circle if we are given that equation of the circle as x^2 +y^2 - 8x +12y = 12

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justaguide | College Teacher | (Level 2) Distinguished Educator

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We need to find the area of the circle x^2 +y^2 - 8x +12y = 12

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

convert it to the form (x - a)^2 + (y - b)^2 = r^2 where r is the radius

=> x^2 - 8x + 16 + y^2 + 12y + 36 = 12 + 16 + 36

=> (x - 4)^2 + (y + 6)^2 = 64 = 8^2

The radius of the circle is 8.

The area of the circle equal to pi*r^2 = 64*pi

The area of the circle is 64*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 - 8x + 12y = 12

We need to rewrite the equation into the standard form in order to determine the radius.

==> (x-a)^2 + (y-b)^2 = r^2

Then we will need to complete the square.

==> x^2 - 8x + 16 -16 + y^2 + 12y + 36 -36 = 12

==> (x-4)^2 + (y+6)^2 = 12 + 36 + 16

==. (x-4)^2 + 9y+6)^2 = 64

==> (x-4)^2 + (y+6)^2 = 8^2

Then the radius is r= 8.

Now we will calculate the area.

==> A= r^2 * pi = 8^2 * pi = 64*pi = 201.06

Then the area of the circle is 64pi = 201.06 square units.

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