Find the area of the circle x^2+y^2 - 2x + 8y = 13

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The equation of the circle is x^2+y^2 - 2x + 8y = 13

x^2+y^2 - 2x + 8y = 13

=> x^2 - 2x +1 +y^2 + 8y + 16 = 13 + 1 + 16

=> (x - 1)^2 + (y + 4)^2 = 30

=> (x - 1)^2 + (y + 4)^2 = (sqrt 30)^2

This is of the form (x - a)^2 + (y - b)^2 = r^2, where r is the radius

The radius of the circle is sqrt 30.

The area is pi*r^2 = pi*30

The circle has an area of 30*pi square units.

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

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Given the equation of the circle is :

x^2 + y62 - 2x + 8y = 13

We need to find the area.

First we need to determine the radius.

Then, we will rewrite the equation into the standard form.

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

To convert, we will need to complete the square.

==> x^2 - 2x + 1 -1 + y^2 + 8y + 16 - 16 = 13

==> (x-1)^2 + (y+4)^2 = 13 + 16 + 1

==> (x-1)^2 + (y+4)^2 = 30

Then the radius is the circle is sqrt30.

Now we will calculate the area.

==> A = r^ 2* pi = sqrt30^2 * pi = 30*pi = 94.25

Then, the area of the circle is 30pi = 94.25 square units.

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