Find the Point(s) on the Surface $x ^ { 2 } + y ^ { 2 } + 4 z ^ { 2 } = 6$

question 7

Essay

Find the point(s) on the surface $x ^ { 2 } + y ^ { 2 } + 4 z ^ { 2 } = 6$ such that the tangent plane at the point is parallel to the plane $x + 2 y - 2 z = 4$

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Definitions:

Heritability

The proportion of variance in a particular trait within a population that is attributable to genetic differences among individuals.

Free Will

The concept that humans have the capacity to choose and act upon their own decision making, free from predestination or determinism.

Humanism

A psychological approach focusing on examining the entire individual and the distinctiveness of each person's experiences.

Psychoanalysis

A therapeutic approach founded by Sigmund Freud focusing on unconscious mental processes and early childhood experiences.