To write the equation of a circle in standard form, we use the formula:
\((x - h)^2 + (y - k)^2 = r^2\)
where \((h, k)\) is the center of the circle and \(r\) is the radius.
Given:
- Center: \((4, -5)\)
- Radius: \(2\)
Substituting these values into the formula:
\[ (x - 4)^2 + (y + 5)^2 = 2^2 \] \[ (x - 4)^2 + (y + 5)^2 = 4 \]
Therefore, the standard form of the equation of the circle is:
\[ (x - 4)^2 + (y + 5)^2 = 4 \]
The correct response is:
left parenthesis x minus 4 right parenthesis squared plus left parenthesis y plus 5 right parenthesis squared equals 4
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