Conic Sections Explorer

Circle - Radius: 100

0:00

Conic Sections Explorer

Conic sections are curves obtained by intersecting a plane with a double-napped cone. These curves have fascinated mathematicians for centuries and have numerous applications in science and engineering.

Types of Conic Sections:

Circle: All points equidistant from a center point
Ellipse: Sum of distances to two foci is constant
Parabola: All points equidistant from a focus and directrix
Hyperbola: Difference of distances to two foci is constant

Mathematical Equations:

Circle: (x-h)² + (y-k)² = r²

Variables Explanation:

• x, y = Coordinates of any point on the curve

• h, k = Coordinates of the center point

• r = Radius of the circle

Ellipse: (x-h)²/a² + (y-k)²/b² = 1

Variables Explanation:

• x, y = Coordinates of any point on the curve

• h, k = Coordinates of the center point

• a = Semi-major axis length

• b = Semi-minor axis length

Parabola: (x-h)² = 4p(y-k)

Variables Explanation:

• x, y = Coordinates of any point on the curve

• h, k = Coordinates of the vertex point

• p = Focal length (distance from focus to vertex)

Hyperbola: (x-h)²/a² - (y-k)²/b² = 1

Variables Explanation:

• x, y = Coordinates of any point on the curve

• h, k = Coordinates of the center point

• a = Semi-transverse axis length

• b = Semi-conjugate axis length

Real-World Applications:

Astronomy: Planetary orbits (ellipses)
Engineering: Satellite dishes (parabolas)
Architecture: Arches and bridges
Physics: Projectile motion (parabolas)

About This Simulation:

This interactive simulation allows you to explore conic sections by adjusting parameters and seeing the changes in real-time. Use the controls to modify the shape, position, and properties of each conic section.

⚙️Controls

Animation Controls

Conic Section Type

Shape Parameters

Radius / Major Axis (a):

100

Minor Axis (b):

Position Controls

Center X Position:

Center Y Position:

Rotation Angle:

0°

Display Options

Show Coordinate Grid

Show Axes

Show Foci Points

Show Equation

Show Calculations

Area:

31415.93 units²

Perimeter/Circumference:

628.32 units

Foci Coordinates:

(0, 0)

Eccentricity:

0.00