Question

What is the directrix of a parabola?

Answer 1

Hint: We first define what a parabola is. Its general equation can be given as ${{y}^{2}}=4ax.$ We then show by means of a diagram what a directrix of a parabola is. Then we explain what is the role of the directrix in a parabola.

Complete step-by-step solution:
In order to answer this question, we define what a parabola is. A parabola is a curvilinear shape where any point on the curve is equidistant from a point called the focus and from a line called the directrix of the parabola. We draw a parabola whose general equation is as follows:
$\Rightarrow {{y}^{2}}=4ax$
Here, a stands for the coordinates of the focus of the parabola. We have drawn the parabolic curve along with the directrix line as shown in the figure below.

As shown in the figure, the directrix is a straight line parallel to the y-axis for the parabola with a general equation of the form ${{y}^{2}}=4ax.$ The coordinates of the directrix is $\left( -a,0 \right).$ Directrix is useful in determining the definition of a parabola. Any point taken on the parabola will be equidistant from two things: The focus and the directrix. Let this point be P. The distance from point P to the focus is same as the perpendicular distance from point P to the line known as the directrix located at a point $\left( -a,0 \right).$
Hence, the directrix is a line parallel to the y-axis and is important for defining the parabolic curve.

Note: It is important to know the basic concepts of parabola and its definition. This will help us solve such questions. One important point to note is that the directrix is always perpendicular to the axis of symmetry of the parabola which is the x-axis in this case.