Verified answer

x = r cos t

and r = f ( theta )

dx / dt = r ( - sin t ) + cos t ( dr / d theta )

dx / dt = (dr / d theta ) cos t - r sin t

y = r sin theta

dy dt = r cos theta + sin theta ( dr / d theta )

dy / dt = (dr / d theta ) sin theta + r cos theta

dy / dx = ( dy / dt ) / (dx / dt )

now to do the substituting.

dy / dt = (- 4 cos theta ) sin theta + ( 5 - 4 sin theta ) cos theta

dy / dt = - 8 sin theta cos thtea + 5

dy / dt = - 4 sin ( 2 theta ) + 5

dx / dt = ( - 4 cos theta ) cos theta - ( 5 - 4 sin theta ) sin theta

dx / dt = - 4 cos (2 theta ) - 5

dy / dx = ( - 4 sin ( 2 theta ) + 5 ) / ( - 4 cos (2 theta ) - 5 )

do what you like with the equations.