Question

Find the equation of a 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

Answer on Question #76925 - Math - Analytic Geometry

Consider the point $(x,y)$:

$$\rho^{2}((x, y); (3, -3)) = (x - 3)^{2} + (y + 3)^{2}$$

The slope of corresponding line equals $\frac{y + 3}{x - 3}$. As a result, we have an equation:

$$(x - 3)^{2} + (y + 3)^{2} = \frac{y + 3}{x - 3}$$