Locus and Straight Line

A locus is a set

A locus is a set of points satisfying certain geometric conditions. For example, the locus of points equidistant from two fixed points A(-3,0) and B(3

Inclination (θ) is the angle

Inclination (θ) is the angle a line makes with positive X-axis (0° ≤ θ < 180°). Slope = tan θ = (y₂-y₁)/(x₂-x₁) for points (x₁,y₁) and (x₂,y₂). Exampl

Two lines are parallel if they

Two lines are parallel if they have equal slopes (m₁ = m₂). Two lines are perpendicular if m₁ × m₂ = -1. Example: Lines with slopes 3 and -1/3 are per

For lines with slopes m₁

For lines with slopes m₁ and m₂, acute angle θ is given by tan θ = |m₁-m₂|/|1+m₁m₂|. Example: Lines with slopes 3 and -2 have angle tan θ = |3-(-2)|/|

Multiple forms exist

Multiple forms exist: (1) Slope-point: y-y₁ = m(x-x₁), (2) Slope-intercept: y = mx+c, (3) Two-point: (y-y₁)/(y₂-y₁) = (x-x₁)/(x₂-x₁), (4) Double-inter