Parabola – Equations and its terms
Standard Equations
of
Y
Y
Y
Y
Parabola
Latus
S Rectum
with
a > 0
Vertix V(0, 0)
S
V
X
V
S
X
X
Latus
Rectum
X
V
V
Latus
Rectum
S
Latus
Rectum
Eccentricity e = 1
Length of Latus
Rectum = 4 a
Focus S
S (a,0)
S (– a,0)
S (0,a)
S (0, –a)
Equation of directrix
x=–a
x+a=0
x=a
x–a=0
y=–a
y+a=0
y=a
y–a=0
Equation of axis
y=0
y=0
x=0
x=0
Equation of latus
rectum
x=a
x–a=0
(x–axis)
(x–axis)
x=–a
x+a=0
(y–axis)
(y–axis)
y=–a
y+a=0
y=a
y–a=0
MUHAMMAD ZAFARULLAH, ASSISTANT PROFESSOR OF MATHEMATICS,
DJ Sindh Govt. Science College, Karachi
Standard Equations
of
Y
Y
Y
Y
Parabola
with
a > 0
Vertix V(h, k)
Axis of
Parabola
Latus
Rectum
V
S
Axis of
Parabola
Latus
Rectum
Eccentricity e = 1
S
V
Axis of
Parabola
X
X
Length of Latus
Rectum = 4 a
Focus S
S (h+a, k)
Equation of directrix x = h – a
Equation of axis
y=k
(parallel to x–axis)
Equation of Latus
x=h+a
Rectum
V
V
Latus
Rectum
X
S
Latus
Rectum
S
X
Axis of
Parabola
S (h – a, k)
x=h+a
y=k
(parallel to x–axis)
x=h–a
S (h, k+a)
x=k–a
x=h
(parallel to y–axis)
y=k+a
S (h, k – a)
x=k+a
x=h
(parallel to y–axis)
y=k–a