The general form of the equation of a circle is given by:
\[ (x - h)^2 + (y - k)^2 = r^2 \]
where \((h, k)\) is the center of the circle and \(r\) is the radius.
Given the center \((6, -1)\) and the radius \(10\), we can substitute these values into the equation:
- \(h = 6\)
- \(k = -1\)
- \(r = 10\)
Now substituting:
\[ (x - 6)^2 + (y + 1)^2 = 10^2 \]
Calculating \(10^2\):
\[ (x - 6)^2 + (y + 1)^2 = 100 \]
This is the equation of the circle in standard form. In general conic form (which typically takes the form \(Ax^2 + By^2 + Cx + Dy + E = 0\)), we can rearrange it:
\[ (x - 6)^2 + (y + 1)^2 - 100 = 0 \]
Expanding this equation gives us:
\[ (x^2 - 12x + 36) + (y^2 + 2y + 1) - 100 = 0 \]
Combining like terms:
\[ x^2 + y^2 - 12x + 2y - 63 = 0 \]
Thus, the general conic form of the equation is:
\[ x^2 + y^2 - 12x + 2y - 63 = 0 \]