The locus procedure is a systematic method for converting geometric conditions into algebraic equations. The four steps -- Let, Express, Eliminate, Replace (mnemonic: LEER) -- provide a reliable framework for all locus problems.

Step 1 (Let): Introduce P(h,k) as a general point on the locus. Using (h,k) instead of (x,y) avoids confusion when the geometric condition involves equations already written in x and y.

Step 2 (Express): Translate the geometric condition (distance, angle, perpendicularity, tangency, etc.) into an algebraic equation involving h, k, and possibly auxiliary parameters.

Step 3 (Eliminate): If the condition introduces parameters (slope of a variable line, parameter of a conic, angle), eliminate them to obtain a relation purely in h and k. Techniques include: solving one equation for the parameter and substituting, using identities like sin^{2+cos}^2=1 for trigonometric parameters, using Vieta's formulas when two parameter values satisfy a quadratic, or squaring and adding.

Step 4 (Replace): Substitute h->x, k->y to state the final locus equation. Verify by checking that specific instances of the geometric condition produce points satisfying the equation.

Common pitfalls: forgetting to check for extraneous solutions introduced during squaring, losing sign information when taking square roots, and including degenerate cases that don't satisfy the original condition.

The parametric approach is often cleaner than the Cartesian approach for conic-related locus problems. Express coordinates in terms of one parameter (like t for the parabola: ($at^2$, 2at)), apply the condition, and eliminate t.