Directrix Parabola Math

In mathematics a parabola is a plane curve which is mirror symmetrical and is approximately u shaped it fits several other superficially different mathematical descriptions which can all be proved to define exactly the same curves.

Directrix parabola math. You probably know that the smaller a in the standard form equation of a parabola the wider the parabola. The parabola is the curve formed from all the points x y that are equidistant from the directrix and the focus. And every parabola is going to have a focus and a directrix because every parabola is the set of all points that are equidistant to some focus and some directrix. Exploring focus directrix relation to graph.

These are all these are all right angles right over here. Converting y2 5x to y2 4ax form we get y2 4 5 4 x so a 5 4 and the focus of y 2 5x is. X 2 2mxy m 2 y 2 2 h m 2 1 mb x 2 k m 2 1 2 b y h 2 k 2 m 2 1 b 2 0. A parabola is a conic section another way of defining a parabola when a plane intersects a cone we get different shapes or conic sections where the plane intersects the outer surface of the cone.

So that s all a focus and a directrix is. This is a graph of the parabola with all its major features labeled. For a given point called the focus and a given line not through the focus called the directrix a parabola is the locus of points such that the distance to the focus equals the distance to the directrix. A parabola can be defined as a curve where any point is at an equal distance from the directrix a line and the focus a point.

Equate the y coordinates and solve for q. Equivalently you could put it in general form. 1 1 p 2 2 1 p p 1. F a 0 5 4 0 the equations of parabolas in different orientations are as follows.

Find the focus for the equation y 2 5x. If f is the focus of the parabola v is the vertex and d is the intersection point of the directrix and the axis of symmetry then v is the midpoint of the line segment f d. A line perpendicular to the axis of symmetry used in the definition of a parabola. A parabola is a locus of points equidistant from a line called the directrix and point called the focus.

Equate the x coordinates and solve for p. In other words y 1x is a wider parabola than y 2x and y 1x is a wider parabola than y 2x. 4 2 q 2 8 2 q q 6. A line used to help define a shape.

Axis of symmetry focus vertex and directrix. Given the focus h k and the directrix y mx b the equation for a parabola is y mx b 2 m 2 1 x h 2 y k 2. Or if the parabola was down here you d go straight up to find that distance. At least i think this last one is right.