consider the curve given by y的平方 =2+xy

consider the curve given by y的平方 =2+xy
(1) show that dy/dx = y/(2y-x)
(2) find all points (x,y) on the curve where the line tagent to the curve has slope 1/2
(3)show that there are no points (x,y) on the curve where the line tangent to the curve is horizontal
(4) let x and y be functions of time t that are related by the equation y的平方 =2+xy.at time t=5,the value of y is 3 and dy/dt=6.find the value of dx/dt at time t=5