Strategy 1 -- Identify the locus type before computing: Many standard geometric conditions immediately reveal the locus type. Equidistant from two points is always a line. Constant ratio of distances from two points (ratio != 1) is always a circle. Sum/difference of distances from two foci is always an ellipse/hyperbola.

Strategy 2 -- Use parametric elimination for conic loci: Express coordinates using one parameter (t for parabola, theta for ellipse/circle), apply the condition, and eliminate the parameter. This avoids messy Cartesian algebra.

Strategy 3 -- For conic identification, compute $h^{2-ab}$ directly: Don't perform the rotation. $h^{2-ab}$<0 (ellipse), =0 (parabola), >0 (hyperbola). Then check Delta for degeneracy.

Strategy 4 -- When a=b, rotate by 45 degrees: This is the most common rotation angle in JEE. It transforms xy-type terms into X^{2-Y}^2 forms and vice versa.

Strategy 5 -- Use invariants to find new coefficients after rotation: A+B=a+b and A*B=ab-$h^2$. Solve the resulting quadratic $t^{2-}$(a+b)t+(ab-$h^2$)=0 for the new coefficients without performing the substitution.

Strategy 6 -- Verify locus equations: Pick a specific instance of the geometric condition, compute the resulting point, and check it satisfies the locus equation. This catches algebraic errors.

Common traps: (1) Squaring both sides introduces extraneous solutions -- check the sign. (2) Division by a variable may lose solutions -- consider the zero case. (3) The locus may exclude certain points that don't satisfy the original condition. (4) When using (h,k), don't forget to replace with (x,y) at the end.