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Homework Statement .

Let ##C_a## a cardioid given in polar coordinates by ##r_a= a+cos(\theta)## with a being a parameter, and ##\theta## ##\in [0,2\Pi]##

a)Prove that, for a>1, ##C_a## is a smooth curve.

b)Calculate the tangent line to the curve ##C_a## in the cartesian coordinates point ##(x,y)=(0,a)##

My problem is I don't understand how this curve is, I mean, I googled and saw how it looks like, but I don't know the parameterization.

By the way, I accidently pressed enter, so I opened an empty thread and I couldn't check the spell in the title, it says "cardiod"", when it should be "cardioid"", does anyone know how can I correct the title?

Let ##C_a## a cardioid given in polar coordinates by ##r_a= a+cos(\theta)## with a being a parameter, and ##\theta## ##\in [0,2\Pi]##

a)Prove that, for a>1, ##C_a## is a smooth curve.

b)Calculate the tangent line to the curve ##C_a## in the cartesian coordinates point ##(x,y)=(0,a)##

My problem is I don't understand how this curve is, I mean, I googled and saw how it looks like, but I don't know the parameterization.

By the way, I accidently pressed enter, so I opened an empty thread and I couldn't check the spell in the title, it says "cardiod"", when it should be "cardioid"", does anyone know how can I correct the title?

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