Write the equations in cylindrical coordinates 7z 2x2 2 y2

Write the equations in cylindrical coordinates. 7z = 2x^2+ 2 y^2 6x^2 + 6y^2 = 5y

Solution

In cylindrical cordinates ,

x = r cos , y = r sin , z = z

b ) 6x² + 6y² = 5y

6( r cos )² + 6( r sin)² = 5( r sin )

6r²cos² + 6r²sin² = 5r sin

6r²(sin² + cos²) = 5r sin

6r²(1) = 5r sin [ Since , in trigonometric identities sin² + cos² = 1 ]

6r² = 5r sin

6r = 5sin

r = (5/6)sin