Part of CG-03 — Parabola

JEE Problem-Solving Strategies

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For JEE parabola problems: (1) Always identify a first — compare with y2y^2=4ax or x2x^2=4ay. (2) Use parametric form (at2at^2, 2at) whenever possible — it simplifies all computations. (3) For tangent problems, choose between point form (T=0), slope form (y=mx+a/m), or parametric form based on what's given. (4) For focal chord problems, immediately use t1t2=-1. (5) For normal problems from an external point, set up the cubic and use Vieta's formulas (sum=0 for parameters). (6) Remember the constant sub-normal = 2a as a quick check. (7) The directrix is the locus of intersection of perpendicular tangents. (8) For locus problems, express the geometric condition in terms of parameter t and eliminate t. (9) Check whether the given point is inside/outside using S1 before attempting tangent/normal problems. (10) The T=0 substitution is universal — use it for chord of contact, chord with midpoint, and pair of tangents.

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