This problem requires us to find the locus of the circumcenter of a variable triangle. The key to solving it involves understanding the properties of tangents to a parabola, determining the triangle's vertices, and recognizing the special case of a right-angled triangle's circumcenter.

1. Key Concepts and Formulas

• Equation of a Tangent to a Parabola: For a parabola of the form $y^2 = 4ax$, the equation of a tangent line in parametric form (using parameter $t$) is given by $ty = x + at^2$ This form is particularly useful as it allows us to represent the varying third side of the triangle using a single parameter.
• Vertices of a Triangle: These are the points where the three side equations intersect. We will find these by