The line perpendicular to line y=x is y=−x+c or x+y−c=0 Given, hyperbola is x2−2y2=18 or
x2
18
−
y2
9
=1 Here, a2=18,b2=9 Condition for tangency of hyperbola is c2=a2m2−b2 c2=18×(−1)2−9 c2=9⇒c=+3 Equation of tangents are x+y±3=0 Distance between tangent =