Coordinate geometry - Coordinates and locus

Coordinate geometry - Coordinate system

• Coordinate geometry - Formula - Distance
• Coordinate geometry - Formula - Section and mid point
• Coordinate geometry - Triangle - Point of concurrence - Types
• Coordinate geometry - Area - Triangle and quadrilateral

Coordinate geometry - Locus

• Coordinate geometry - Locus - Equation
• Coordinate geometry - Locus - Equation - Parametric and Cartesian

Coordinate geometry - Straight line

Straight line - Classification

• Straight line - Slope and intercepts
• Straight line - Equation - Slope, intercept and point form
• Straight line - Equation - Two point and intercept form
• Straight line - Equation - General and normal form
• Straight line - Angle of intersection
• Straight line - Point of intersection
• Straight line - Concurrency and sign
• Straight line - Perpendicular - Length, foot and image

Straight line - Pair

• Straight line - Pair - Equation - Through origin
• Straight line - Angle between the lines ax² + 2hxy + by² = 0
• Straight line - Pair of lines - Angle between
• Straight line - Parallel - Pair
• Straight line - Parallel - Distance between
• Straight line - Parallel - Angle - Bisector
• Straight line - Equation - General - Second degree
• Straight line - Homogenization

Transformation of axes

• Translation of axes
• Rotation of axes

Coordinate geometry - Circles and system of circles

Circles

• Circles - Equation - Standard and central form
• Circles - Equation - Diameter form
• Circles - Equation - General form
• Circles - Equation - Parametric form
• Circles - Touching - Condition
• Circles - Tangent - Equation
• Circles - Tangent - y = mx + c to x² + y² = a²
• Circles - Tangent - Length
• Circles - Power of a point
• Circles - Chord - Equation
• Circles - Chord of Contact
• Circles - Normal, pole and polar - Equation
• Circles - Points and lines - Conjugate

System of circles

• System of circles - Relative position
• System of circles - Common chord - Angle between
• System of circles - Orthogonal
• System of circles - Axis and center - Radical
• System of circles - Coaxial system
• System of circles - Coaxial system - Limiting points

Coordinate geometry - Conic section

Conic section - Parabola

• Parabola - Equation - Standard - Derivation
• Parabola - Equations - Other forms
• Parabola - Vertex at any point
• Parabola - Tangent and normal - Equation
• Parabola - Tangent - y = mx + c to parabola - Condition
• Parabola - Equation - Pole, polar, parametric form and chords

Conic section - Ellipse

• Ellipse - Equation - Standard - Derivation
• Ellipse - Equation - Other forms
• Ellipse - Tangent and normal - Equation
• Ellipse - Tangent - y = mx + c to ellipse - Condition
• Ellipse - Pole, polar, conjugate points & lines and chords
• Ellipse - Equation - Parametric form

Conic section - Hyperbola

• Hyperbola - Equation - Standard - Derivation
• Hyperbola - Equation - Other forms
• Hyperbola - Equation - Tangent and normal
• Hyperbola - Tangent - y = mx + c to hyperbola - Condition
• Hyperbola - Pole and polar, conjugate points & lines and chords
• Hyperbola - Equation - Director, auxiliary circle, parametric
• Coordinate geometry - Asymptotes

Polar coordinates

• Coordinates - Polar and Cartesian - Relation
• Polar coordinates - Distance formula, triangle area
• Polar Equation - Line, circle, conic

Three dimensional coordinate system

Geometry - Three dimensional - Coordinates and position vector

• Three dimensional geometry - Distance formula
• Three dimensional geometry - Section and mid point formulae
• Three dimensional geometry - Centroid - Triangle, tetrahedron

Three dimensional geometry - Direction cosines and ratios

Straight line - Direction cosines

• Straight line - Direction cosines - Relation
• Straight line - Direction Ratios
• Straight line - Angle between two lines & Lagrange's identity

Three dimensional geometry - Projections

• Straight line - Projection - Point on a line and plane
• Straight line - Projection - Line segment on a line

Three dimensional geometry - Plane

Plane - Equations

• Plane - Equations - General, vector and Cartesian - Normal form
• Plane - Equations - Reduction of General to Normal form
• Plane - Equations - Passing through a given point
• Plane - Equations - Passing through three points
• Plane - Equation - Through two points and parallel to a vector
• Plane - Equations - Intercept form
• Planes - Angle between
• Angle - Between a line and a plane
• Plane - Distance of a point
• Plane - Equation - Passing through the intersection of two planes

Three dimensional geometry - Sphere

Sphere - Equations

• Sphere - Equations - Vector
• Sphere - Equations - Cartesian form
• Sphere - Equations - General form
• Sphere - Equations - Extremities of diameter given