JEE Tips for Locus and Transformation

Always use (h,k) for the moving point to avoid variable confusion.
For conic locus problems, the parametric approach (express everything in terms of one parameter, then eliminate) is usually cleaner than the Cartesian approach.
When asked to "identify the conic," first check $h^{2-ab}$ . Then compute Delta to check degeneracy.
Rotation by 45 degrees is the most common: it converts xy= $c^2$ to $X^{2-Y}^2$ =2 $c^2$ .
Translation is needed whenever the conic is not centered at origin — look for the center by solving partial derivatives = 0.
Verify your locus: pick a specific instance of the geometric condition, compute the point, and check it satisfies your locus equation.