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# Mathematics! Calculus?

Find the equation of the tangent plane and the equation of the normal line at the

point P0(1, 0, 1) on the surface (x, y, z) such that 3z+x^2=4

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- Anonymous9 years agoFavorite Answer
The gradient of the surface is ∇f=( 2x, 0, 3 ). Evaluating at the point (1,0,1) gives ∇f=(2,0,3) as the surface normal. The tangent plane therefore has the form 2x+3z=b, and substituting the known point gives 2(1)+3(1)=b, thus:

Tangent plane: 2x + 3z = 5

Normal line: ( 1+2t, 0, 1+3t )

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