Question
A circle is centered at (−3, 2) and has a radius of 2. Which of the following is the equation for this circle? (5 points)
(x + 3)2 + (y − 2)2 = 2
(x − 3)2 + (y + 2)2 = 4
(x + 3)2 + (y − 2)2 = 4
(x − 3)2 + (y + 2)2 = 2
(x + 3)2 + (y − 2)2 = 2
(x − 3)2 + (y + 2)2 = 4
(x + 3)2 + (y − 2)2 = 4
(x − 3)2 + (y + 2)2 = 2
Answers
GPT-4o mini
To write the equation of a circle, we use the standard formula:
\[
(x - h)^2 + (y - k)^2 = r^2
\]
where \((h, k)\) is the center of the circle and \(r\) is the radius.
In your case, the center of the circle is \((-3, 2)\), which means \(h = -3\) and \(k = 2\). The radius \(r\) is given as \(2\). Therefore, \(r^2 = 2^2 = 4\).
Plugging in the values into the formula, we have:
\[
(x - (-3))^2 + (y - 2)^2 = 4
\]
This simplifies to:
\[
(x + 3)^2 + (y - 2)^2 = 4
\]
So, the correct equation for the circle is:
\[
(x + 3)^2 + (y - 2)^2 = 4
\]
Thus, the correct option from your list is:
**(x + 3)² + (y − 2)² = 4**.
\[
(x - h)^2 + (y - k)^2 = r^2
\]
where \((h, k)\) is the center of the circle and \(r\) is the radius.
In your case, the center of the circle is \((-3, 2)\), which means \(h = -3\) and \(k = 2\). The radius \(r\) is given as \(2\). Therefore, \(r^2 = 2^2 = 4\).
Plugging in the values into the formula, we have:
\[
(x - (-3))^2 + (y - 2)^2 = 4
\]
This simplifies to:
\[
(x + 3)^2 + (y - 2)^2 = 4
\]
So, the correct equation for the circle is:
\[
(x + 3)^2 + (y - 2)^2 = 4
\]
Thus, the correct option from your list is:
**(x + 3)² + (y − 2)² = 4**.