Coordinate Geometry

The slope (m) of a line

The slope (m) of a line is defined as tan θ, where θ is the angle of inclination with the positive x-axis. For a line passing through points (x₁, y₁)

Lines can be represented in multiple

Lines can be represented in multiple forms: Point-slope form (y - y₁ = m(x - x₁)), Slope-intercept form (y = mx + c), Intercept form (x/a + y/b = 1),

The perpendicular distance from a point

The perpendicular distance from a point P(x₁, y₁) to a line Ax + By + C = 0 is given by d = |Ax₁ + By₁ + C|/√(A² + B²). This formula is derived using

Circles can be represented as

Circles can be represented as: Standard form (x² + y² = r²) for center at origin, Central form ((x-h)² + (y-k)² = r²) for center at (h,k), Diameter fo

A parabola is the set

A parabola is the set of all points equidistant from a fixed point (focus) and a fixed line (directrix). The standard equations are: y² = 4ax (opens r