The correct option is A x−2y+8=0
x−y+2=02x−y−2=0}
Solving the two equations, we get
x=4 and y=6
So, the tangent passes through (4,6)
Let slope of the tangent be m.
y−6=m(x−4)
⇒y=mx+6−4m which is tangent to the parabola y2=8x
∴6−4m=2m [Using c=am]
⇒3m−2m2=1
⇒2m2−3m+1=0
⇒m=12,1
For m=12,
y=12x+6−2
⇒x−2y+8=0
For m=1,
y=x+2 that is the given line itself.
So, tangent is :x−2y+8=0