Part of CG-03 — Parabola

Overview of Parabola

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The parabola is a conic section with eccentricity exactly 1. It appears in JEE Main as 1-2 questions per year, typically testing tangent/normal equations, focal chord properties, and parametric problems. The standard form y2y^2 = 4ax encodes the key parameter 'a' which determines the focus (a,0), directrix x=-a, and latus rectum 4a. Unlike the ellipse and hyperbola, the parabola has no centre and extends to infinity. Its unique properties — constant sub-normal, reflection through focus, perpendicular tangents at focal chord endpoints — make it rich in problem variety. The parametric representation (at2at^2, 2at) is the most powerful tool, converting all problems to single-variable algebra. The T=0 substitution rule connects tangent, chord of contact, and chord with midpoint formulas into a unified framework shared with all conics.

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