Answer :
To determine the center and radius of the circle from the given equation, we start by recalling the standard form of a circle's equation:
[tex]\[ (x - h)^2 + (y - k)^2 = r^2 \][/tex]
In this form, \((h, k)\) represents the center of the circle, and \(r\) represents the radius.
Given the equation:
[tex]\[ (x - 13.4)^2 + (y + 2.6)^2 = 100 \][/tex]
First, we identify the components that correspond to \(h\), \(k\), and \(r^2\):
- The term \((x - 13.4)^2\) indicates that \(h = 13.4\).
- The term \((y + 2.6)^2\) indicates that \(k = -2.6\) (since it can be rewritten as \((y - (-2.6))^2\)).
- The right side, 100, represents \(r^2\).
Next, we solve for \(r\) by taking the square root of 100:
[tex]\[ r = \sqrt{100} = 10.0 \][/tex]
Therefore:
1. The center of the circle is \((h, k) = (13.4, -2.6)\).
2. The radius is \(r = 10.0\) units.
So, our final answers are:
- Center: \( (13.4, -2.6) \)
- Radius: [tex]\( 10.0 \)[/tex] units
[tex]\[ (x - h)^2 + (y - k)^2 = r^2 \][/tex]
In this form, \((h, k)\) represents the center of the circle, and \(r\) represents the radius.
Given the equation:
[tex]\[ (x - 13.4)^2 + (y + 2.6)^2 = 100 \][/tex]
First, we identify the components that correspond to \(h\), \(k\), and \(r^2\):
- The term \((x - 13.4)^2\) indicates that \(h = 13.4\).
- The term \((y + 2.6)^2\) indicates that \(k = -2.6\) (since it can be rewritten as \((y - (-2.6))^2\)).
- The right side, 100, represents \(r^2\).
Next, we solve for \(r\) by taking the square root of 100:
[tex]\[ r = \sqrt{100} = 10.0 \][/tex]
Therefore:
1. The center of the circle is \((h, k) = (13.4, -2.6)\).
2. The radius is \(r = 10.0\) units.
So, our final answers are:
- Center: \( (13.4, -2.6) \)
- Radius: [tex]\( 10.0 \)[/tex] units
