A [b]cardioid [/b]is a two-dimensional plane figure that has a heart-shaped curve. The word “cardioid” originated from a Greek word, which means “heart”. Hence, it is called a heart-shaped curve. The shape of a cardioid can be compared to the cross-section of an apple excluding its stalk.[br][br]It is a form of a sinusoidal spiral. This curve is the inverse of a parabola having focus at the centre of inversion. A cardioid does have exactly 3 parallel tangents with any particular gradient. It has a cusp (formed by the intersection of two branches of a curve). The length of the passing through the cusp of the cardioid is 4a, where “a” be the circle radius.[br][img]https://cdn1.byjus.com/wp-content/uploads/2021/10/Cardioid-1.png[/img][br][br]

[b]The polar equation of the horizontal cardioid is given by:[br][/b][math]r=a\left(1\pm cos\theta\right)[/math][b][br]The polar equation of the vertical cardioid is given by:[br][/b][math]r=a\left(1\pm sin\theta\right)[/math][b][br][/b]

[list][size=150][*][b]a[/b] is a constant that is a constant that determines the size of the cardioid.[br][/*][*][b]n[/b] is the number of quater cycles the curve is shifted.[/*][*][b]v[/b] is the upper limit of the parameter t, it represents the endpoint of the interval over which you want to trace or display the curve.[/*][/size][/list]

Type "Polar SG1" to find in phone app.[br][u][color=#0000ff]https://www.geogebra.org/3d/nc3zbjke[/color][/u]