The parametric equations are and .

Find the points at which the tangent is horizontal.

For Horizontal tangent: .

Consider .

Apply derivative on each side with respect to .

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Equate to .

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Horizontal tangents are at .

Find the point of horizontal tangency.

At :

.

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At , the point is .

At :

.

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At , the point is .

Horizontal tangent line occur at and .

For vertical tangent: .

Consider .

Apply derivative on each side with respect to .

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Equate to .

.

At :

.

.

At , the point is .

Vertical tangent line occur at .

Graph:

Graph the parametric equations and .

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Horizontal tangent line occur at and .

Vertical tangent line occur at .