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Parabola

DEFINITION :-

        A Parabola is the collection of all points P in the plane that are the same distance from a fixed point F as they are from a fixed line D. The point F is called the focus of the parabola, and the line D is its directrix .

Basic Formulae Of Parabola

S.No
Equation
Vertex
Focus
Directrix Equation
Equation of Axis of Symmetry
Length of Latus Rectum
Equation of Latus Rectum
1
y2=4ax
(0,0)
(a,0)
x=-a
y=0
4a
x=a
2
y2=-4ax
(0,0)
(-a,0)
x=a
y=0
4a
x=-a
3
x2=4ay
(0,0)
(0,a)
y=-a
x=0
4a
y=a
4
x2=-4ay
(0,0)
(0,-a)
y=a
x=0
4a
y=-a
5
(y-k)2=4a(x-h)
(h,k)
(h+a,k)
x=h-a
y = k
4a
x=h+a
6
(y-k)2=-4a(x-h)
(h,k)
(h-a,k)
x=h+a
y=k
4a
x=h-a
7
(x-h)2=4a(y-k)
(h,k)
(h,k+a)
y=k-a
x=h
4a
y=k+a
8
(x-h)2=-4a(y-k)
(h,k)
(h,k-a)
y=k+a
x=h
4a
y=k-a

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