To find the equation of the tangent plane to the surface x = h(y, z) at the point (2, -5, 0), we can use the formula for the equation of a plane in three-dimensional space. The equation of a plane is given by:
\[ a(x - x_0) + b(y - y_0) + c(z - z_0) = 0 \]
where (x_0, y_0, z_0) is a point on the plane and (a, b, c) is a vector normal to the plane.
Given that x = h(y, z) is the parametrized surface, we can write the equation of the tangent plane at the point (2, -5, 0) as:
\[ h_y(y,z)(y - (-5)) + h_z(y,z)(z - 0) = 0 \]
Now, substitute the values of h_y and h_z at the point (-5,0) into the equation:
\[ 3(y + 5) + 5z = 0 \]
Simplify the equation:
\[ 3y + 15 + 5z = 0 \]
\[ 3y + 5z = -15 \]
Therefore, the equation of the tangent plane to the surface x = h(y, z) at the point (2, -5, 0) is 3y + 5z = -15.Answer:
Step-by-step explanation:
