# 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.
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Usamah Prosser
$f\left(x,y,z\right)=7xy+yz+4xz-48=0$ (2,2,2)
Tangent direction is $\left({P}_{x},{P}_{y},{P}_{z}\right)$

at (2,2,2)

(22,16,10)
$⇒x\left(t\right)=\left(2,2,2\right)+t\left(22,16,10\right)$
$⇒22\left(x-z\right)+16\left(y-z\right)+10\left(z-z\right)=0$
$22x+16y+10z-96=0$