The parabola is the locus points which are equidistant from the other, called the focus F and a line called the directrix d. Similarly is the locus of the centers of tangent circles incidents adequate focus.
Throughout the vertex V parabola equidistant from focus and guideline: dV = VF, remains the guideline a line perpendicular to the axis of the curve, which is its axis of symmetry.
To trace perpendicular to the axis are different (eg straight), take the distance perpendicular to the guidance given, and that radio is a circle with center at F and da radio. The 2 points of intersection are given and symmetrical points of the curve.
We can see an example with numbers: for any point, 5 for example, make a perpendicular to the axis. 5H with distance (from point 5 to the guideline D) center in F do and where to cut perpendicular through the point 5 are the 2 points of the parabola.
2 lines that are cut are listed in order of increasing and decreasing in the same number of points. They join the following points: 1 with 1, 2 to 2, etc., The resulting curve is the envelope of the parabola tangent to the 2 original lines.
2 are divided horizontal and vertical lines in the same number of points as in Fig.
points on the horizontal and vertical are plotted on the horizontal points are straight to the top of the parabola. The intersection of the 2 radiation are the points of the parabola.
2 intersecting straight fall into the same number of points in the order of the figure, for example from 0 to 9. Point 0 of a line joins with the other line, and point 9 of the other with all points on the other line. The intersection of the 2 radiation are the points of a parabola.
equidistant lines and circles in the intersection of each line in each circle are the points of parabolic curves.
If two axes ab P whose intersection is divided into equal segments (1, 2, 3 , 4 ,...) from P and a random point M a (to the right of a, like in the picture) we circumferences passing through 1, 2, 3, 4, and M get circles that cut the line b in D, V, etc. At the intersection of these circles and b we cut horizontal to vertical in 1 2 3 4 points of the parabola.
All parabolas have the same shape in the drawing parabolas look the same but at different distances. If we take one of them and always comes out just climbed to the previous form and they are all proportional. Are therefore the parables in this curve equal to the circumference, They are also always the same way although they may have different sizes.
Given the focus of the parabola and two points of the AB, to determine the axis, the vertex and directrix of the parabola. We can
arc of 90 ° for AF, that is, make a circle whose diameter is the focus F and a point A. We
another circle passing through the focus F and the other point B.
construct a tangent line, in red, the two circles and we focus perpendicular to the tangent obtained in this way at their intersection the vertex V of the parabola. The line passing through the vertex and the focus is the core of it, to get the guidance we center at the vertex and taking the distance as the radius of the vertex V to the focus F, we make an arc intersecting the axis at this distance VF . At that intersection make a perpendicular to the axis-green-and that is the directrix of the parabola. The resolution of the exercise is based on the whole tangent to the parabola intersects the red line that passes through the vertex, a point which, together with the focus, we have that is perpendicular to the tangent.
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