Axis Of Symmetry Of Parabola
Axis of symmetry of parabola divides the parabola into two congruent parts. The Axis of symmetry is generally the axis of the parabola and it cut the parabola at its vertex. The axis of symmetry of a standard parabola having the equation y^{2} = 4ax is the xaxis.The axis of symmetry of parabola divides the parable into two rectangular arcs.
Let us learn more about the axis of symmetry of parabola with the help of examples, FAQs.
What Is Axis Of Symmetry Of Parabola?
The axis of symmetry of parabola is a line that cuts the parabola into two equal halves. Generally, the axis of symmetry of parabola is nothing but the axis of the parabola. The axis of the parabola cuts the parabola at its vertex and is passing through the focus of the parabola.
Let us check the axis of symmetry of the parabola for the standard set of parabolas.
 For the parabola y^{2} = 4ax the axis of symmetry of parabola is the xaxis and its equation is y = 0.
 For the parabola y^{2} = 4ax the axis of symmetry of parabola is the xaxis and its equation is y = 0.
 For the parabola x^{2} = 4ay the axis of symmetry of parabola is the yaxis and its equation is x = 0.
 For the parabola x^{2} = 4ay the axis of symmetry of parabola is the yaxis and its equation is x = 0.
Properties Of Axis Of Symmetry Of Parabola
The following are the important properties of the axis of symmetry of parabola.
 The axis of symmetry is generally the axis of the parabola.
 The vertex and the focus lies on the axis of symmetry of parabola.
 The axis of symmetry of parabola is perpendicular to the latus rectum.
 The axis of symmetry of parabola is perpendicular to the directrix.
Terms Related To Axis Of Symmetry Of Parabola
The following important terms are related to the axis of symmetry of the parabola.
 Vertex of Parabola: The vertex of the parabola is the point where the parabola cuts the axis of the parabola. The parabola y^{2} = 4ax cuts the axis at the origin, and (0, 0) is the vertex of the parabola.
 Focus of Parabola: The focus of a parabola lies on the axis of the parabola. The parabola y^{2} = 4ax has the xaxis as the axis of the parabola and (a, 0) is the focus of the parabola.
 Latus Rectum of Parabola: The line passing through the focus and perpendicular to the axis of the parabola is called the latus rectum of parabola. The parabola y^{2} = 4ax has the latus rectum of length 4a units.
 Directrix Of Parabola: The directrix is a line perpendicular to the axis of parabola and is outside the parabola. For the parabola y^{2} = 4ax the equation of directrix is x + a = 0. Also as per definition, the parabola is the locus of a point that is equidistant from the focus and the directrix.
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Examples of Axis Of Symmetry Of Parabola

Example 1: Find the axis of symmetry of parabola x^{2} = 12y.
Solution:
The given equation of parabola x^{2} = 12y can be compared with the standard equation of the parabol x^{2} = 4ay.
This parabola represents an inverted U form of a parabola with the yaxis as its axis.
Hence the given equation has the yaxis as its axis of symmetry.

Example 2: Find the equation of a parabola having the axis of symmetry of the parabola as the xaxis, having the origin as the vertex, and the focus is (5, 0).
Solution:
The equation of a parabola with xaxis as the axis of symmetry and having its vertex at (0, 0) is of the form y^{2} = 4ax.
The focus of this parabola is (a, 0) = (5, 0), and hence a = 5. Substituting the value of 'a' in the equation of parabola we have the following equation.
y^{2} = 4(5)x
y^{2} = 20x
Therefore the required equation of the parabola is y^{2} = 20x.
FAQs on Axis Of Symmetry Of Parabola
What Is Axis Of Symmetry Of Parabola?
The axis of symmetry of the parabola is the line that cuts the parabola into two equal halves. The axis of symmetry of the parabola \(y^2 = 4ax\) is the xaxis and it divides the parabola into two parts in the first and the fourth quadrant. The axis of symmetry of parabola is sometimes referred to as the axis of parabola.
How To Find Axis Of Symmetry Of Parabola?
The axis of symmetry of the parabola can be easily found from the geometric representation of parabola in the coordinate axis. The axis of symmetry of a parabola \(y^2 = 4ax\) is the xaxis, as the xaxis cuts the parabola into two equal halves.
What Is The Equation Of Axis Of Symmetry Of Parabola?
The axis of symmetry for a parabola \(y^2 = 4ax\) is the xaxis and its equation is y = 0. And the axis of symmetry of the parabola \(x^2 = 4ay\) is the yaxis and its equation is x = 0.
Is The Axis Of Parabola Also The Axis Of Symmetry Of Parabola?
The axis of symmetry of parabola is the same as the axis of the parabola.
How Many Axis Of Symmetry Does A Parabola Have?
The parabola has only one axis of symmetry. The one axis of symmetry cuts the parabola into two equal halfs.For a standard equation of parabola \(y^2 = 4ax\), the xaxis represented by the equation y = 0 is the only axis of symmetry of parabola.
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