1. Which of the following is an equation of the plane tangent to the surface x2 + y2 – 3z = 2 at the point (-2, -4, 6) ?
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A. x +y +z –2 = 0 |
B. –2x –4y +6z = 0 |
C. –2x –4y +6z –2 = 0 |
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D. 4x +8y +3z = 0 |
E. 4x +8y +3z +22 = 0 |
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Solution: The answer is E
By definition, an equation of the tangent plane to the surface z = f(x,y) at the point P(x0,y0,z0) is given by,
Thus, given the surface, x2 + y2 – 3z = 2, solve for z in terms of x and y and let z = f(x,y). As follows,
Then,
Hence, the equation of the plane tangent to the given surface at the point (-2, -4, 6) can be found by substituting the corresponding values into the above definition of the tangent plane. As follows,
