Find Equations for the Tangent Plane and the Normal Line $x y + y z + x z = 38$

question 70

Multiple Choice

Find equations for the tangent plane and the normal line to the surface with equation $x y + y z + x z = 38$ at the point $P ( 2,4,5 )$

• A) \(6 x + 7 y + 9 z = 76\) , \(\frac { x - 2 } { 6 } = \frac { y - 4 } { 7 } = \frac { z - 5 } { 9 }\)
• B) \(9 x + 7 y + 6 z = 76\) , \(\frac { x - 2 } { 9 } = \frac { y - 4 } { 7 } = \frac { z - 5 } { 6 }\)
• C) \(2 x + 4 y + 5 z = 76\) , \(\frac { x - 6 } { 2 } = \frac { y - 7 } { 4 } = \frac { z - 9 } { 5 }\)
• D) \(2 x + 4 y + 5 z = 76\) , \(\frac { x - 9 } { 2 } = \frac { y - 7 } { 4 } = \frac { z - 6 } { 5 }\)

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Definitions:

Person-Centered Therapy

A form of psychotherapy developed by Carl Rogers that emphasizes the importance of being in a conducive environment provided by a supportive therapist for an individual's growth and self-improvement.

Unconditional Positive Regard

An attitude of total acceptance toward another person regardless of their actions or feelings.

Person-Centered Therapy

A form of psychotherapy that emphasizes the importance of an individual's subjective experience and the therapist's unconditional positive regard toward the client.

Incongruence

A state in which there is a mismatch between one's experiences and self-image or between one's self-image and ideal self.