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You probably know that the smaller a in the standard form equation of a parabola the wider the parabola.
Parabola directrix math. You can understand this widening effect in terms of the focus and directrix. If the line 8x y 4 0 is a tangent to the parabola find the value of k. A parabola is set of all points in a plane which are an equal distance away from a given point and given line. A parabola is defined as follows.
This is a graph of the parabola with all its major features labeled. For horizontal parabolas the vertex is x a y k 2 h where h k is the vertex. I understand that the parabola has vertex 0 and is concave up i gathered that from a quick sketch but i m not sure what to do beyond that. 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.
The axis of symmetry is located at y k. In other words y 1x is a wider parabola than y 2x and y 1x is a wider parabola than y 2x. Axis of symmetry focus vertex and directrix. One way we can define a parabola is that it is the locus of points that are equidistant from both a line called the directrix and a point called the focus.
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. The equation of a parabola is in the form y kx 2. A line used to help define a shape. Y 2 0.
The point is called the focus of the parabola and the line is called the directrix. Would really appreciate some help. The directrix is perpendicular to the axis of symmetry of a parabola and does not touch the parabola.
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