Find the Equation for the Plane Tangent to the Parametrized

question 43

Essay

Find the equation for the plane tangent to the parametrized surface S at the point P.
- $$\mathrm { S } \text { is the cone } \mathbf { r } ( \mathrm { r } , \theta ) = \mathrm { r } \cos \theta \mathbf { i } + \mathrm { r } \sin \theta \mathbf { j } + 4 \mathrm { rk } ; \mathrm { P } = ( - 5 \sqrt { 2 } , 5 \sqrt { 2 } , 40 ) \text {. }$$

---

Definitions:

Scarification

Decorative markings on the human body made by cutting or piercing the flesh to create scars.

Beauty and Status

Concepts often intertwined, where societal perceptions of beauty can influence an individual's social status and vice versa, varying greatly across different cultures and historical periods.

Horned Headdress

A type of headwear that includes representations of horns, often associated with deities, royalty, or warriors in various cultures.

Tassili n'Ajjer

A plateau in the Sahara desert in southeastern Algeria, known for its prehistoric rock art and unique geological formations.