The straight line $L_1$ touches the curves $y^2=4x$ at $A$ and $x^2=4y$ at $B$.The straight line $L_2$ is normal to both the curves cutting the first curve at $C$ and $D$ and the second curve at $E$ and $F$.Find the area bounded by $L_1$ and the coordinate axes and the area bounded by $L_2$ and the coordinate axes.
This question is given in my book in the solved examples.Solution is like this.
Since $x^2=4y$ and $y^2=4x$ are mirror images of each other in line $x=y$.Therefore the slopes of common tangent and common normal are $-1$ each.
I did not understand this line.Why the slopes of common tangent and common normal are $-1$ each?If this concept had been clear,rest of the solution is understandable.Please help me understand this concept.
Does it help to see the graphs?