Given a Quadratic Bezier Curve $a$ defined with three points $A$, $Q$, and $B$.
Then given a point $P$ such that $P\in a$. The task is to find such a Quadratic Bezier Curve $b$ that is defined by points $A$, $K$, and $P$ (where $K$ is some unknown control point) and any of the points of this curve is a point of $a$ curve.
Could anyone please suggest a way to determine the point K, if all other points are given?