Coordinate Geometry.

Question

The straight line L₁ touches the parabolas y²=4ax at A and x²=4ay at B. The Straight line L₂ is normal to the two parabolas cutting them at points C,D,E,F. 
C being in 4th quadrant and F in 2nd quadrant. Then Prove-

1. The equation of L₁ is : x+y+2a=0
2. The equation of L₂ is : x+y -3a=0