Given : y2=x−1 and x2=y−1
By observation, if we swap x by y in y2=x−1, then we get x2=y−1
So, they are symmetric about y=x
Finding the equation of tangents on both the curve which is parallel to y=x
Now for y2=x−1,
2yy′=1⇒y′=12y=1⇒y=12⇒x=54⇒x−y−34=0
Now for x2=y−1,
y′=2x⇒2x=1⇒x=12⇒y=54⇒x−y+34=0
Distance between parallel lines
=∣∣
∣
∣
∣∣−34−34√12+12∣∣
∣
∣
∣∣=3√24
Hence, a+b=7