The correct option is D x−2y+8=0
Equation of tangent in term of slope of
y2=8x is
y=mx+2m⋯(i)
∵ Angle between (i) and y=3x+5 is 45∘, then
⇒∣∣∣m−31+3m∣∣∣=tan45∘=1⇒±(m−3)=1+3m
When m−3=1+3m
∴m=−2
When −m+3=1+3m
∴m=12
Now, the equation of tangents are
y=−2x−1 and y=x2+4⇒2x+y+1=0 and x−2y+8=0