Locus

A set of points in a plane which satisfy certain geometrical condition (or conditions) is called a locus.

L = {P | P is a point in a plane and P satisfy given geometrical condition} Here P is the representative of all points in L.

The circle with center O and radius 4 is the set L = { P | OP = 4, P is a point in the plane }

Set of points on a circle

The perpendicular bisector of segment AB is the set M = { P | P is a point in a plane such that PA = PB }.

Perpendicular bisector

Examples:

​Some important pointers about slope.

General form of a line:

ax + by = c

Slope intercept form of a line: y = mx + c

Point-slope form of a line: y - y₁ = m (x - x₁)

Two point form of a line:
(y - y₁) ∕ (x - x₁)= (y₂ - y₁ ) ∕ (x₂ - x₁)

Double-intercept form of a line:
x ∕ a + y ∕ b = 1

xcosα + ysinα = p

Normal form of a line: