Terms Related
to an Ellipse:
Fundamental
Terms
|
Ellipse
(Horizontal ellipse)
|
Conjugate
Ellipse(Vertical ellipse)
|
|
(a)
|
Equation
|
x²/a² + y²/b² =
1 (a > b)
|
x²/a² + y²/b² =
-1 (a < b)
|
(b)
|
Graph
|
 |
 |
(c)
|
Centre
|
C(0, 0)
|
C(0, 0)
|
(d)
|
Vertices
|
(±a, 0)
|
(0, ±b)
|
(e)
|
Length of major
axis
|
2a
|
2b
|
(f)
|
Length of minor
axis
|
2b
|
2a
|
(g)
|
Foci
|
(±ae, 0)
|
(0, ±be)
|
(h)
|
Equation of
directrices
|
X = ±(a/e)
|
Y = ±(b/e)
|
(i)
|
Eccentricity
|
e = √(1 -
[b²/a²])
|
e = √(1 - [a²/b²])
|
(j)
|
Length of
latusrectum
|
2b²/a
|
2a²/b
|
(k)
|
Ends of
latusrectum
|
(±ae, ±b²/a)
|
(±a²/b, ±be)
|
(l)
|
Parametric
equations
|
 |
|
(m)
|
Parametric
coordinates
|
acosα, bsinα
|
acosα, bsinα
|
(n)
|
Focal distance
or radii
|
|SP| = (a -
ex₁) and |S’P| = (a + ex₁)
|
|SP|=(b - ey₁)
and |S’P| = (b + ey₁)
|
(o)
|
Sum of local
radii |SP| + |S’P|
|
2a
|
2b
|
(p)
|
Distance
between foci
|
2ae
|
2be
|
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