We will discuss about the standard form of parabola y\(^{2}\) = - 4ax

The equation y\(^{2}\) = - 4ax (a > 0) represents the equation of a parabola whose co-ordinate of the vertex is at (0, 0), the co-ordinates of the focus are (- a, 0), the equation of directrix is x = a or x - a = 0, the equation of the axis is y = 0, the axis is along negative x-axis; the length of its latus rectum is 4a and the distance between its vertex and focus is a.

Solved example based on the standard form of parabola y\(^{2}\) = - 4ax:

Find the axis, co-ordinates of vertex and focus, length of latus rectum and the equation of directrix of the parabola y\(^{2}\) = -12x.

**Solution:**

The given parabola y\(^{2}\) = -12x.

⇒ y\(^{2}\) = - 4 ∙ 3 x

Compare the above equation with standard form of parabola y\(^{2}\) = - 4ax, we get, a = 3,

Therefore, the axis of the given parabola is along negative x-axis and its equation is y = 0

The co-ordinates of its vertex are (0, 0) and the co-ordinates of its focus are (-3 , 0); the length of its latus rectum = 4a = 4 ∙ 3 = 12 units and the equation of its directrix is x = a i.e., x = 3 i.e.,x - 3 = 0.

**● ****The Parabola**

**Concept of Parabola****Standard Equation of a Parabola****Standard form of Parabola y22 = - 4ax****Standard form of Parabola x22 = 4ay****Standard form of Parabola x22 = -4ay****Parabola whose Vertex at a given Point and Axis is Parallel to x-axis****Parabola whose Vertex at a given Point and Axis is Parallel to y-axis****Position of a Point with respect to a Parabola****Parametric Equations of a Parabola****Parabola Formulae****Problems on Parabola**

**11 and 12 Grade Math**__From Standard form of Parabola y^2 = - 4ax____ to HOME PAGE__

**Didn't find what you were looking for? Or want to know more information
about Math Only Math.
Use this Google Search to find what you need.**

## New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.