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To find the center and radius of the circle from the equation \(x^2 + y^2 + 4x - 10y - 7 = 0\), we first need to convert it into the standard form of a circle's equation: \((x - h)^2 + (y - k)^2 = r^2\). Identifying the center as \((h, k)\) and the radius as \(r\) becomes straightforward once in this format. The goal is to manipulate the given equation to express it in the standard form through appropriate algebraic steps. The speaker emphasizes the necessity of achieving this rearrangement to easily determine the circle's key characteristics.
