# Cardioid

Cardioid
Field: Geometry
Image Created By: Wolfram Math World

Cardioid

The Cardioid an epicycloid with one cusp.

# Basic Description

The image is formed by tracing a point on the circumference of a circle of radius $a$, without slipping, on another stationery circle, as in the image below

.

# A More Mathematical Explanation

The curve is given by:

• Cartesian equation $({x^2} + {y^2} - 2ax)^2 = 4{a^2}({x^2} + {y^2})$, where '"UNIQ--math-00 [...]

The curve is given by:

• Cartesian equation $({x^2} + {y^2} - 2ax)^2 = 4{a^2}({x^2} + {y^2})$, where $a$ is the radius of the moving circle.
• Polar equation $r = a (1 - {\cos} {\theta})$
• Parametric equations

$x = a {\cos} t (1 - {\cos t})$ $y = a {\sin} t (1 - {\cos t})$

## Properties

• It has a cusp at the origin.

# Teaching Materials

  [[Description::The Cardioid an epicycloid with one cusp.|]]
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