Thus if x is first replaced with x+ˉg/ˉc and y with y+ˉf/ˉc, 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.
The parabola can be defines as the limiting curve of an ellipse as one focus (in the case we’re examining, that would be F1) going to infinity. The eccentricity evidently goes to one, e→1 since th...The parabola can be defines as the limiting curve of an ellipse as one focus (in the case we’re examining, that would be F1) going to infinity. The eccentricity evidently goes to one, e→1 since the center of the ellipse has gone to infinity as well.