1
CONIC SECTION FORMULAS CLASS XI
Let l be a fixed line and F be a fixed point not on l, and e > 0 be a fixed real number. Let |MP| be the perpendicular
distance from a point P (in the plane of the line l and point F) to the line l, then the locus of all points P such that |FP|
= e |MP| is called a conic.
Main facts about the parabola
Equations
y²= 4ax
,
(a>0)
Right hand
y² = -4ax ,a>0
Left hand x² = 4ay ,a>0
Upwards x² = -4ay ,a>0
Downwards
Axis
y=0
y = 0
x = 0
x = 0
Eqn. of
Directrix
x +a = 0
x
-
a = 0
y +a = 0
y
-
a = 0
Focus
(a, 0)
(
–
a, 0)
(0,a)
(0,
–
a)
Verte
x
(0,0)
(0,0)
(0,0)
(0,0)
Length of Latus
-
rectum
4a
4a
4a
4a
Main facts about the ellipse
Equation
x²/a² + y²/b² = 1
(
a > b
)
x²/a² + y²/b² = 1 (a < b)
Eccentricity
b
2
= a
2
(
1
–
e
2
)
a
2
= b
2
(
1
–
e
2
)
Equation of major axis
y = 0
x = 0
Length of major axis
2a
2b
Equation of minor axis
x = 0
y = 0
length of minor axis
2b
2a
V
ertices
(
± a,0)
(0, ± b
)
Foci
(
±
ae, 0)
(0,
±
b
e)
Equation of
Directrices
x = ±
a/e
y
= ±
b/
e
Length of Latus
-
rectu
m
2b²/a
2a²/b
The fixed point F is called a
focus
of the conic and the fixed line
l
is
called the directrix associated with F. The fixed real number e (> 0) is
called eccentricity of the conic.
In particular, a conic with eccentricity e is called
(i) a parabola iff e = 1 (ii) an ellipse iff e < 1 (iii) a hyperbola iff e > 1.
