Browse Formulas by Category
Geometry is the foundation of mathematics that deals with shapes, sizes, and properties of space. Whether you’re solving problems for academic purposes, engineering, architecture, or just curious about the wonders of geometry, having a handy collection of formulas is essential. This page is your one-stop destination for geometry formulas related to shapes and solids.
Points
Learn how to represent and work with points in analytic geometry using coordinate systems. Includes distance and midpoint formulas.
A Triangle
Explore formulas for area, centroid, and side lengths of triangles given vertices. Useful in coordinate geometry applications.
- Key Formula
- Collinearity and Triangle Conditions
- Distance and Side Lengths
- Section Formula and Division of Line Segments
- Centroid (Center of Mass)
- Circumcenter and Circumcircle
- Incenter and Incircle
- Orthocenter and Altitudes
- Special Triangle Types
- Medians and Their Properties
- Angle Calculations
- Slope and Angle Between Lines
- Line Equations for Triangle Sides
- Translation and Transformation
Equation of Line
Master equations of lines in slope-intercept, point-slope, and general form. Essential for analytic geometry and algebra.
- Key Formula - Slope-Intercept Form
- Different Forms of Line Equations
- Line Joining Two Points
- Line Through Point Parallel to Given Line
- Line Through Point Perpendicular to Given Line
- Slope and Direction
- Distance and Angle Relationships
- Parallel and Perpendicular Lines
- Parametric and Vector Forms
- Special Line Cases
- Converting Between Forms
Equation of Circle
Understand how to write and analyze the equation of a circle using its center and radius in Cartesian coordinates.
Ellipse
Study the standard equation of an ellipse, including foci, axes lengths, and coordinate geometry properties.
Hyperbola
Learn the equation of a hyperbola in standard form, including definitions of foci, axes, and asymptotes.
Parabola
Explore parabola equations and their focus, vertex, and axis. Useful for algebra and geometric analysis.
- Key Formula - Standard Form
- Standard Equation
- Different Orientations of Parabolas
- Area of Segment Bounded by a Parabola
- Translated Parabola
- Eccentricity of a Parabola
- Focus and Directrix
- Distance from a Point on Parabola to Focus
- Parametric Equations
- Vertex Form and Quadratic Function
- Important Properties and Measurements
Line
Understand geometric properties of lines including angle between lines, perpendicular distance, and intersections.
Equation of Line Joining Two Points A,B
Find the equation of a line joining two given points A and B using slope formula and point-slope form.
Plane
Learn the equation of a plane in three dimensions, including normal form and point-normal form.
Equation of Sphere Center at M and Radius R in Rectangular Coordinates
Explore the formula for a sphere with a given center and radius in rectangular (Cartesian) coordinates.
Equation of Ellipsoid With Center M and Semi-Axes A,B,C
Understand the ellipsoid equation centered at M with semi-axes A, B, and C in 3D space.
Elliptic Cylinder With Axis as Z Axis
Explore the analytic geometry of an elliptic cylinder aligned with the Z-axis using standard equations.
Elliptic Cone With Axis as Z Axis
Understand the equation of an elliptic cone whose axis of symmetry lies along the Z-axis.
Hyperboloid of One Sheets
Study the equation of a hyperboloid of one sheet and understand its surface properties in 3D.
Hyperboloid of Two Sheets
Learn about hyperboloids of two sheets with examples and standard equation format in analytic geometry.
Elliptic Paraboloid
Explore the 3D surface represented by an elliptic paraboloid. Includes standard form and axis orientation.
Hyperbolic Paraboloid
Understand the equation and shape of a hyperbolic paraboloid, a saddle-shaped 3D surface in geometry.
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📖 Bookmark This PageEssential Analytical Geometry Concepts
📍 Coordinate Systems
Master Cartesian, polar, cylindrical, and spherical coordinate systems for spatial analysis.
📏 Distance & Position
Calculate distances, midpoints, and relative positions using coordinate-based methods.
⭕ Curves & Surfaces
Understand equations of circles, conics, and 3D surfaces through algebraic representations.
🔄 Transformations
Apply coordinate transformations for rotation, translation, and scaling of geometric objects.
Analytical Geometry Study Tips
Visualize Coordinate Systems
Always sketch coordinate axes and plot points to understand spatial relationships and geometric concepts.
Master Distance & Midpoint
These fundamental formulas form the basis for most analytical geometry problems and applications.
Connect Algebra to Geometry
Understand how algebraic equations represent geometric shapes and spatial relationships.
Practice 3D Visualization
Develop spatial reasoning skills by working with 3D coordinate systems and surface equations.
Real-World Applications
GPS & Navigation
Calculate positions, distances, and optimal routes using coordinate geometry and spatial analysis techniques.
Computer Graphics & Gaming
Create 3D models, implement transformations, render scenes, and design interactive virtual environments.
Engineering & CAD
Design mechanical parts, architectural structures, analyze spatial relationships, and optimize geometric configurations.
Aerospace & Robotics
Calculate trajectories, control robotic movements, design spacecraft paths, and analyze 3D spatial dynamics.
Quick Reference Guide
Analytical geometry bridges algebra and geometry by using coordinates to study geometric properties and relationships. Whether you're working with 2D coordinate planes or 3D spatial analysis, these formulas provide the mathematical foundation for computer graphics, engineering design, navigation systems, and scientific modeling. From basic distance calculations to complex surface equations, analytical geometry offers precise tools for spatial problem-solving.