Consider the surface z=(x/2)^2-(y/3)^2. Compute the tangent plane at each point. Find the point such that the normal vector is vertical at that point.

Deborah Proctor

Deborah Proctor

Answered question

2022-10-17

Consider the surface z = ( x 2 ) 2 ( y 3 ) 2 . Compute the tangent plane at each point. Find the point such that the normal vector is vertical at that point.

Answer & Explanation

Plutbantonavv

Plutbantonavv

Beginner2022-10-18Added 15 answers

Given surface
z = ( x 2 ) 2 ( y 3 ) 2
tangent plane at each point
Here f ( x , y , z ) = ( x 2 ) 2 + ( y 3 ) 2 z
let a point in given surface, whose posiion vector is
r 0 = a i + b j + c k
let p be any point of tangent plane
( r r 0 ) f = 0 ( ( x a ) u + ( y b ) j + ( z j k ) ) ( x a ) x 2 + 2 ( y b ) y 9 ( z c ) x ( x a ) 2 + 2 y 9 ( y b ) ( z c )
This is the equation of tangent plane at each point.

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?