Parabola is a conic section. It is defined as the set of all points whose distance from a fixed point, called the focus, is equal to the distance from a fixed line, called the directrix.
The eccentricity, e of a parabola is equal to 1.
|Focus (F)||\(a\) distance from the vertex.|
|Latus Rectum (LR)||\(LR~=~4a\)
A line segment passing through the focus and parallel to the directrix.
|\(a\)||distance between the vertex and the focus or the distance between the directix and the vertex.|
\( Ax^2 + Dx + Ey + F = 0\) or \(Cy^2 +Dx + Ey + F = 0\)
Where A, B, C, D E and F are constants.
|Vertex at \( (0,0) \)|
|\(y^2 = 4ax\)||Opens Upwards|
|\(y^2 = -4ax\)||Opens Downwards|
|\(x^2 = 4ax\)||Opens to the right|
|\(x^2 = -4ax\)||Opens to the left|
|Vertex at \( (h,k) \)|
|\( (y-h)^2 = 4a(x-k)\)||Opens Upwards|
|\((y-h)^2 = -4a(x-k)\)||Opens Downwards|
|\( (x-k)^2 = 4a(y-h)\)||Opens to the right|
|\((x-k)^2 = -4a(y-h)\)||Opens to the left|