Write the equations in cylindrical coordinates.
(a) 6x + 5y + z = 6
(b) −4x^2 − 4y^2 + z^2 = 5

In cylindrical coordinates, we take
x = r cos(t)
y = r sin(t)
z = z
(a) Then
6x + 5y + z = 6
transforms to
6r cos(t) + 5r sin(t) + z = 6
(b) We have
x² + y² = r² (cos²(t) + sin²(t)) = r²
so
-4x² - 4y² + z² = 5
converts to
-4r² + z² = 5