Question

What is the equation of a circle with center (2,-3) and radius 3?O -A. (x - 2)2 +(y +37- 3B. (x + 2)2 + (y - 3y - 9O C. (x - 2)2 +(y +3j? = 9x 2 2D. (x - 2) - (+31° - 9

Answer 1

The Equation of a Circle

Given a circle of radius r and centered at the point (h, k), the equation of the circle is:

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

Please, note the value of the coordinates of the center appear with its signs changed.

We have to find the equation of this circle by substituting the values of r = 3 and (h, k) = (2, -3). Substituting:

`\begin{gathered} (x-2)^2+(y+3)^2=3^2 \\ \text{Operating:} \\ (x-2)^2+(y+3)^2=9 \end{gathered}`

Choice C.