Question

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

Answer 1

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`