How do you write the standard form of the equation of the circle with Center: (3, -2); Radius: 3?

1 Answer
striker4150
Dec 13, 2015

The standard form of the equation of the circle would be #(x - 3)^2 + (y + 2)^2 = 9#.

Explanation:

The standard form of the equation of a circle is:

#(x - x_1)^2 + (y - y_1)^2 = r^2#

#x# and #y# are the #x# and #y# variables, #x_1# is the x-coordinate of the center, #y_1# is the y-coordinate of the center, and #r# is the radius of the circle.

In order to place the center of the circle at point (3, -2), simply replace #x_1# with 3 and #y_1# with -2.

The equation is now:

#(x - 3)^2 + (y - (-2))^2 = r^2#

This can be simplified as:

#(x - 3)^2 + (y + 2)^2 = r^2#

Finally, replace #r# with the radius of the circle.

#(x - 3)^2 + (y + 2)^2 = 3^2#.

The final equation is:

#(x - 3)^2 + (y + 2)^2 = 9#

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