Locus and transformation appear as 0-1 questions per year in JEE Main, often embedded within conic section problems. They are tested more frequently as part of broader coordinate geometry questions rather than standalone.
Most common formats: (1) "Find the locus of a point satisfying [condition]." Direct application of the LEER procedure. (2) "Identify the conic represented by [equation]." Compute and Delta. (3) "After rotation/translation, the equation becomes..." Apply the transformation formulas.
High-frequency sub-topics: Locus of midpoint of chords (using T=S1), locus of intersection of perpendicular tangents (director circle), locus of foot of perpendicular from focus to tangent (auxiliary circle), and conic identification from general second-degree equations.
Typical difficulty: These problems are usually medium difficulty. The algebra is straightforward but requires careful computation. The most common error is incorrect sign handling during parameter elimination.
Time management: Locus problems typically take 3-4 minutes. If the algebra becomes excessively complex, reconsider the approach -- there is usually a cleaner method.
Key formulas to memorize: (1) Rotation angle: tan(2*theta)=2. (2) Translation coordinates: X=x-h, Y=y-k. (3) Reflection across Ax+By+C=0: x'=x-2A. (4) Conic classification: . (5) Degeneracy: Delta=abc+2fgh-af^{2-bg}^{2-ch}^2=0. (6) Director circle of ellipse: x^{2+y}^2=a^{2+b}^2.
Exam tip: In MCQ format, use invariants to eliminate wrong options quickly. If the problem asks for the conic type after transformation, the invariants immediately give the answer without performing the transformation.