The correct option is B 23x−3y−22=0
Equation of the hyperbola is 5x2−y2=5⇒x21−y25=1
Here, a2=1 and b2=5
Equation of the tangent is y=mx±√a2m2−b2 and it passes through (2,8)
∴8=2m±√m2−5
⇒(8−2m)2=m2−5
⇒64+4m2−32m=m2−5
⇒3m2−32m+69=0
⇒3m2−9m−23m+69=0
⇒(3m−23)(m−3)=0
∴m=233,3
Therefore, equation of required tangent's are
y=3x+2 and 23x−3y−22=0