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Finding tangent plane equation of curve z = x ^ 2-y ^ 2 parallel to plane 2x + 4y-z = 0
Tangent plane equation of surface z = x ^ 2-y ^ 2 parallel to plane 2x + 4y-z = 0
z`(x)=2x,z`(y)=-2y
The tangent plane is parallel to the plane 2x + 4y-z = 0
Normal vector (2x, - 2Y, - 1) / / (2,4, - 1) 2x / 2 = - 2Y / 4 = - 1 / (- 1)
Tangent point x = 1, y = - 2, z = 1 + 2 = 3
Tangent plane equation 2 (x-1) + 4 (y + 2) - (Z-3) = 0
2x+4y-z+9=0
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