Parametric forms

Parametric forms Conic Parametric equations Parameter Range of parameter Any point on the conic Circle cos θ sin θ ‘ θ ’ or ( cos , sin ) Parabola at at = −∞< < ∞ ‘ t ’ or at at Ellipse cos θ sin θ ‘ θ ’ or ( cos , sin ) Hyperbola sec θ tan θ except θ = ± ‘ θ ’ or ( sec , tan ) Identifying the conic from the general equation of conic Ax Bxy Cy Dx Ey F The graph of the second degree equation is one of a circle, parabola, an ellipse, a hyperbola, a point, an empty set, a single line or a pair of lines. When, ( ) A C B D h E k F h the general equation reduces to h , which is a circle.