Terms Related to an Ellipse:
Fundamental Terms |
Ellipse (Horizontal ellipse) |
Conjugate Ellipse(Vertical ellipse) |
|
(a) |
Equation | \(\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1(a>b)\) |
\(\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1(a<b)\) |
(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 | \(e=\sqrt{1-\frac{{{b}^{2}}}{{{a}^{2}}}}\) |
\(e=\sqrt{1-{{\left( \frac{a}{b} \right)}^{2}}}\) |
(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 |