Parabola

Parabola can be defined as the conic section created by Intersection of a plane which is parallel to the generator line of surface and a Right Circular Cone. The other definition of parabola: A Plane Curve obtained by the moving a Point which is at fixed distance from a fixed point and also equals to the distance form a fixed line is known as parabola. Now we will see how to draw a parabola.

For drawing parabola we need to follow some steps which are given below:
Step 1: First we take a ‘diretrix’ or a Line Segment.

Step 2: Then we draw focal point named as ‘F’.

Step 3: If we want the vertex then we bisect the distance between line P and focal point ‘F’.

Step 4: Then we draw vertical lines of any distance and name them A, B, C, D, E.

Step 5: Then we measure the distance from Line Segment ‘P’ to the point ‘A’.

Step 6: Then we measure the distance from line segment to the point ‘B’ and repeat the same procedure till the last point.

Step 7: We draw the point from the line segment.

Step 8: At last we join all the points and we get parabola.

Now we will see the general form of parabola:
The general form is:
=> (αp + βq)² + γp + δq + ∈= 0;
This above equation is obtained from the general conic equation which is given below:
=> Ap²+ Bpq + Cq² + Dp + Eq + F = 0;
And the equations for a general form of parabola maths with the focus point F(s, t) and a directrix in the form:
=> pa + qy + c = 0;
Is
=> (pa + qy + c)² = (p - s)² + (q - t)²
        P² + q²
This is the equation of parabola in maths.