Question
What is the center and radius of the circle with equation (x + 9)2 + (y + 5)2 = 64?
center (5, 9); radius = 8
center (−9, −5); radius = 8
center (9, 5); radius = 64
center (−9, −5); radius = 64
center (5, 9); radius = 8
center (−9, −5); radius = 8
center (9, 5); radius = 64
center (−9, −5); radius = 64
Answers
Answered by
GPT-4o mini
To find the center and radius of the circle given by the equation \((x + 9)^2 + (y + 5)^2 = 64\), we can use the standard form of the equation of a circle, which is:
\[(x - h)^2 + (y - k)^2 = r^2\]
where \((h, k)\) is the center of the circle and \(r\) is the radius.
From the equation \((x + 9)^2 + (y + 5)^2 = 64\), we can identify the following:
- The term \((x + 9)\) can be rewritten as \((x - (-9))\), which means \(h = -9\).
- The term \((y + 5)\) can be rewritten as \((y - (-5))\), which means \(k = -5\).
- The right side of the equation, \(64\), is equal to \(r^2\). Therefore, to find the radius \(r\), we take the square root of \(64\), which is \(r = 8\).
Thus, the center of the circle is \((-9, -5)\) and the radius is \(8\).
The correct answer is:
**center (−9, −5); radius = 8**.
\[(x - h)^2 + (y - k)^2 = r^2\]
where \((h, k)\) is the center of the circle and \(r\) is the radius.
From the equation \((x + 9)^2 + (y + 5)^2 = 64\), we can identify the following:
- The term \((x + 9)\) can be rewritten as \((x - (-9))\), which means \(h = -9\).
- The term \((y + 5)\) can be rewritten as \((y - (-5))\), which means \(k = -5\).
- The right side of the equation, \(64\), is equal to \(r^2\). Therefore, to find the radius \(r\), we take the square root of \(64\), which is \(r = 8\).
Thus, the center of the circle is \((-9, -5)\) and the radius is \(8\).
The correct answer is:
**center (−9, −5); radius = 8**.