Part of CG-04 — Ellipse

Overview of Ellipse

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The ellipse is a conic section with eccentricity strictly between 0 and 1. It appears in JEE Main as 1-2 questions per year, typically testing tangent/normal equations, eccentricity calculations, focal properties, and director/auxiliary circle applications. The standard equation x2x^2/a2a^2 + y2y^2/b2b^2 = 1 (a > b > 0) encodes all key parameters: foci at (+/-ae, 0), directrices at x = +/-a/e, and latus rectum 2b2b^2/a. Unlike the parabola, the ellipse is a closed bounded curve with a centre. Its defining property SP + SP' = 2a (sum of focal distances is constant) drives most problem-solving. The parametric form (acos(theta), bsin(theta)) and the T=0 substitution framework connect tangent, normal, chord of contact, and chord-midpoint formulas. The director circle and auxiliary circle provide elegant locus results for perpendicular tangents and eccentric angle geometry.

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