Equation in standard form

Ellipse of Class 11

Equation In Standard Form

x2/a2 + y2/b2 = 1, where b2 = a2(1 − e2) and a > b.

(a) center: (0, 0)

(b) foci: (± ae, 0)

(c) Directrices: x = ± a/e

(d) vertices: (± a, 0)

(e) Equation of major axis is y = 0

Length of Major axis = 2a

(f) Equation of minor axis is x = 0

Length of minor axis is 2b.

(g) Length of latus rectum is 2b2/a

General Equation

ax2 + 2hxy + b y2 + 2gx + 2fy + c = 0 represents an ellipse if   h2 < ab and abc + 2fgh − af2 −bg2 − ch2 ≠ 0.

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