Question

Find an equation of the plane tangent to the following surface at the given point. 7xy+yz+4xz-48=0;\ (2,2,2)

Find an equation of the plane tangent to the following surface at the given point.
\(7xy+yz+4xz-48=0;\ (2,2,2)\)

Answers (1)

2021-06-05
\(f(x,y,z)=7xy+yz+4xz-48=0\) (2,2,2)
Tangent direction is \((P_x,P_y,P_z)\)
\(P_x=7y+yz,\ P_y=7x+z,\ P_z=y+4x\)
at (2,2,2)
\(P_x=22,\ P_y=16,\ P_z=10\)
(22,16,10)
\(\Rightarrow x(t)=(2,2,2)+t(22,16,10)\)
\(\Rightarrow22(x-z)+16(y-z)+10(z-z)=0\)
\(22x+16y+10z-96=0\)
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