Thus if \(x\) is first replaced with \(x + \bar{g} / \bar{c}\) and \(y\) with \(y + \bar{f}/\bar{c}\), and then the new \(x\) is replaced with \(x \cos θ − y \sin θ\) and the new \(y\) with \(x \sin θ...Thus if \(x\) is first replaced with \(x + \bar{g} / \bar{c}\) and \(y\) with \(y + \bar{f}/\bar{c}\), and then the new \(x\) is replaced with \(x \cos θ − y \sin θ\) and the new \(y\) with \(x \sin θ + y \cos θ\), the Equation will take the familiar form of a conic section with its major or transverse axis coincident with the \(x\) axis and its centre at the origin.
