A parabola is collection of all points in a airplane which room an equal distance away from a given suggest and provided line. The point is dubbed the focus that the parabola, and also the line is referred to as the directrix .

The directrix is perpendicular come the axis of the contrary of a parabola and also does not touch the parabola. If the axis of the opposite of a parabola is vertical, the directrix is a horizontal heat .

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If we take into consideration only parabolas that open upwards or downwards, then the directrix is a horizontal line of the form y = c .

Relation between focus, vertex and directrix:

The crest of the parabola is at same distance between focus and the directrix.

If F is the emphasis 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 heat segment F D ¯ .

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Example:

If a parabola has actually a upright axis that symmetry v vertex at ( 1 , 4 ) and also focus in ~ ( 1 , 2 ) , uncover the equation that the directrix.

If F is the emphasis of the parabola, V is the vertex and also D is the intersection point of the directrix and also the axis the symmetry, climate V is the midpoint the the heat segment F D ¯ .

Equate the x -coordinates and also solve for ns .

1 = 1 + ns 2 2 = 1 + p p = 1

Equate the y -coordinates and also solve for q .

4 = 2 + q 2 8 = 2 + q q = 6

The equation that the directrix is that the form y = c and also it passes with the point ( 1 , 6 ) . Here, c = 6 .

So, the equation of the directrix is y = 6 .

The graph is together shown.

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