Final answer:
To find the equation of the tangent plane to the sphere, we use the coefficients of x, y, and z in the sphere's equation as the normal vector components. The equation for the plane is then derived using the point-normal form, but a specific point on the sphere is needed to write the exact equation.
Step-by-step explanation:
The question provided concerns finding the equation of the tangent plane to a given sphere. The equation of the sphere is 2x + y - 2z + 4 = 0. To find the equation of the tangent plane, we first need to identify the normal vector to the surface at a given point. The coefficients of x, y, and z in the equation of the sphere represent the components of the normal vector. Thus, the normal vector is .
To write the equation of the tangent plane, we use the point-normal form: A(x - x_0) + B(y - y_0) + C(z - z_0) = 0, where <(A, B, C)> is the normal vector and <(x_0, y_0, z_0)> is a point on the sphere that lies on the tangent plane. Since the question did not provide specific points, we cannot give the exact equation of a specific tangent plane without additional information.