Locus and Slope of line

Locus and Slope of line

Locus

Let a point be moving under some constant conditions. Then the path traced by the point is called its locus.

Let (h, k) be the coordinates of the point at any instance. On applying the conditions under which the point is moving, we get some equations involving h, k and some parameters. Eliminate all the parameters to obtain a relation between h and k. Then on replacing h by x and k by y, we get the equation of the locus of the point.

Slope of a Line

Slope or gradient of a line joining two points (x₁, y₁) and (x₂, y₂) is denoted conventionally by m = tanθ where θ ≠ π/2 (0 ≤ θ < π) is the angle which the line makes with the positive direction of x-axis and is given by
m = , where x₁≠x_2.