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Compute the equation of the plane tangent to the surface x^2+3 y^2+z^3 = 8 at the point (2,1,1).
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- Find a vector equation for the curve of intersection between the surfaces y^2-x^2=9 and 2x-3y-z=12.Find an equation of the tangent z = 4x² - y² + 2y, plane to the given surface at the specified point. (-2, 4, 8)Determine an equation for the plane that's tangent to the surface z = 6x2 + 7y2 at point (-3, -2, 82)
- Find a parametric equation for the line that is perpendicular to the graph of the equation 4x^2 + 2y^2 +3z^2 = 39 at the points (1,2,3). Use t as the variableFind the equation of the tangent plane to the surface x² + y² + y² + z² = −1 at the point (2, −3, 4)Find the vector equation that represents the curve of intersection of the paraboloid z=3x^2+y^2 and the surface y=x^3. Write the equation so that one of the functions is simply t.
- Find the equation of the plane tangent to the surface of Z = x^2 + y^2 at point P(1, 2, 5).Find an equation for the tangent plane to the surface z = 3y^2 − 2x^2 + x atP(2, −1, −3). Express your answer in the form z = ax + by + c.The equation of the tangent plane to the surface at the point (-2, 1, 3) is Select one: 8 +2y- = -(x-2) + 2(y + 1) - (z + 3) = 0 -(x + 2) + 2(y-1)-(2-3) = 0 -(x + 2) + 2(y-1)-(2-3) = 2/ z-3 x1/2 = 22² =222332 -2/3 None of them 3