Loci

This is the foundational step for finding the path (locus) traced by a moving point. You label the target moving point as $P(x, y)$ and express the given geometric conditions as an equation in $x$ and $y$.

This method handles locus problems involving an extra parameter, such as $t$. By eliminating the parameter $t$ from the parametric equations for $x$ and $y$, you obtain a direct relationship between $x$ and $y$.

This verification step ensures that all points on the derived curve satisfy the original geometric conditions. If the parameter restricts the range of $x$ or $y$, or excludes specific points, they must be clearly stated.