Consider the parabola y = x 2 Since all parabolas are similar, this simple case represents all others Construction and definitions The point E is an arbitrary point on the parabola The focus is F, the vertex is A (the origin), and the line FA is the axis of symmetry The line EC is parallel to the axis of symmetry and intersects the x axisIn this case, the equation of the parabola comes out to be y 2 = 4px where the directrix is the verical line x=p and the focus is at (p,0) If p > 0, the parabola "opens to the right" and if p 0 the parabola "opens to the left" The equations we have just established are known as the standard equations of a parabolaLike the ellipse and hyperbola, the parabola can also be defined by a set of points in the coordinate planeA parabola is the set of all pointslatex\,\left(x,y\right)/latex in a plane that are the same distance from a fixed line, called the directrix, and a fixed point (the focus) not on the directrix
Solved Find The Vertex Focus And Directrix Of The Chegg Com
