0The general equation of a conic is ax2 + 2hxy + by2 + 2gx + 2fy +c =0.
Here if e =1 where e is eccentricity and D≠ 0, then it represents a parabola
The general equation of parabola is (y-y0)2 = (x-x0), which has its vertex at (x0, y0).
The general equation of parabola with vertex at (0, 0) is given by y2 = 4ax, and it opens rightwards.
The parabolax2 = 4ay opens upwards.
The equation y2 = 4ax is considered to be the standard equation of the parabola for which the various components are
Vertex at (0,0)
Directrix is x+a = 0
Axis is y = 0
Focus is (a, 0)
Length of latus rectum = 4a
Ends of latus rectum are L (a, 2a) and L’(a, -2a)
The parabola y = a(x – h)2 + k has its vertex at (h, k)
