What is the equation of a circle with center (3, 2) and radius 4

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baxthum8's profile pic

baxthum8 | High School Teacher | (Level 3) Associate Educator

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The equation of a circle with center (h, k) and radius r is given by this general equation.

`(x - h)^2 + (y - k)^2 = r^2`

Since the center is (3, 2) and radius is 4 we'd get the following by substituting (3, 2) for (h, k) and 4 for r^2.

`(x - 3)^2 + (y - 2)^2 = 4^2`

Therefore,  the equation for the circle with center (3, 2) and radius 4 is:

`(x - 3)^2 + (y - 2)^2 = 16`

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justaguide | College Teacher | (Level 2) Distinguished Educator

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

If the center of the circle is (3, 2) and radius is 4, the equation of the circle is:

(x - 3)^2 + (y - 2)^2 = 4^2

=> x^2 - 6x + 9 + y^2 - 4y + 4 = 16

=> x^2 + y^2 - 6x  - 4y - 3 = 0

The equation of a circle with center (3, 2) and radius 4 is x^2 + y^2 - 6x  - 4y - 3 = 0

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atyourservice | Student, Grade 11 | (Level 3) Valedictorian

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 (x - h)^2 + (y - k)^2 = r^2

 (3(h), 2(k))

plug the number into the formula:

 (x - 3)^2 + (y - 2)^2 = 4^2

 (x - 3)^2 + (y - 2)^2 = 16 is the equation or x^2 +y^2  + 9 + 4 = 16 

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