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 | \(\left\{ \begin{align} & x=a\cos \alpha \\ & y=b\sin \alpha \\\end{align} \right\}\) |
\(\left\{ \begin{align} & x=a\cos \alpha \\ & y=b\sin \alpha \\\end{align} \right\}\) |
|
(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 |