Question

Find the equation of the locus of a point so that the square of its distance from (3, -3) is always numerically equal to the slope of the line joining it to the same point.

Answer 1

$\displaystyle \text{Consider the point(x,y):}\\ p^2((x,y);(3,-3)) = (x-3)^2 + (y+3)^2\\ \text{The slope of corresponding line equals $\frac{y+3}{x-3}$. As a result, we have an equation:}\\ (x-3)^2 + (y-3)^2=\frac{y+3}{x-3}$