Question

Find the equation of the tangent
plane and normal line to the
surface 2x²+ y +2z=3 at point (2, 1,-3)​

Answer 1

Answer:

We have,

f(x,y,z)=2x^2 +y^2 +2z=3

∂f/∂x =4x,  ∂f/∂x =2y, ∂f/∂x =2z

​At point (2,1,−3)

∂f/∂x  =8,  ∂f/∂x =2,  ∂f/∂x  =2

Equation of tangent plane

8(x−2)+2(y−1)+2(z+3)=0

4x+y+z−6=0

Equation of normal is  

x−2/8  =y−1  /2  = z+3 /2

Then,

We get  

x−2/4  = y−1 /1 = z+3 /1

​