Parabola Calculator

This is the conic-section side of a parabola: the ones that open left and right, and the ones described by a focus and a directrix rather than by a formula. Enter x = ay^2 + by + c, or a focus with the line it is measured against, or a vertex with its focus, and it returns the conic form (y - k)^2 = 4p(x - h), the vertex, the axis of symmetry, p, the focus, the directrix, the latus rectum, the intercepts, the domain and range, and a plot with all of them marked. For an upright parabola given as y = ax^2 + bx + c, the quadratic graphing calculator already answers that from the same inputs. A focus set diagonally from its vertex describes a rotated parabola, which is refused rather than guessed at.