Find the Equation of the Tangent Plane To $x ^ { 2 } + 2 x y + 4 y + 6 = z ^ { 2 }$

question 56

Multiple Choice

Find the equation of the tangent plane to $x ^ { 2 } + 2 x y + 4 y + 6 = z ^ { 2 }$ at the point (-4, 1, 3) .

• A) \(6 x + 4 y + 6 z = - 4\)
• B) \(- 6 x + 4 y + 6 z = - 2\)
• C) \(6 x - 4 y + 6 z = - 2\)
• D) \(6 x + 4 y + 6 z = 2\)
• E) \(6 x + 4 y + 6 z = - 2\)

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Definitions:

Photosynthesis

A process by which green plants and some other organisms use sunlight to synthesize foods from carbon dioxide and water. Photosynthesis in plants generally involves the green pigment chlorophyll and generates oxygen as a by-product.

Oxygen Atoms

Fundamental components of molecules, essential for respiration in organisms and a key element in the Earth's atmosphere.

Proton Gradient

The gradient of hydrogen ions (protons) across a membrane, which is a form of potential energy used for ATP production in cells.

Photosynthesis

The process by which green plants, algae, and some bacteria transform light energy into chemical energy stored in glucose, using carbon dioxide and water and releasing oxygen as a byproduct.