⁦Conic sections and the parabola⁩

⁦Cut a cone with a plane and the cut is a curve called a conic section⁩. ⁦The parabola, ellipse and hyperbola are conic sections, and each can be defined by distances from fixed points or a fixed line⁩.

⁦A parabola is the set of points equally far from a fixed point F (the focus) and a fixed line D (the directrix)⁩: MF = MK. ⁦With the vertex at the origin and focus F(p,٠), the directrix is x = −p and the equation is y^٢ = ٤px⁩.

⁦With vertex S(h,k) and the parabola opening up or down, the equation is (x − h)^٢ = ٤p(y − k); the focus is F(h,k + p) and the directrix y = k − p⁩. ⁦If p is positive the parabola opens upwards⁩.