Shortest distance occurs along common normal
Equation of normal at y2=4x having slope m is
y=mx−2m−m3 and point of contact is (m2,−2m)
For y=mx−2m−m3=m(x−3)+m−m3 to be notrmal to y2=2(x−3),
m−m3=−2(12)m−12m3
⇒2m−m32=0
⇒m=0,±2
Point of contact for two parabolas are (m2,−2m) and (3+12m2,−m)
For m=0
Point of contact are (0,0) and (3,0), and shortest distance will be 3
For m=2
Point of contact are (4,−4) and (5,−2), and shortest distance will be √5
For m=−2
Point of contact are (4,4) and (5,2), and shortest distance will be √5
∴ shortest distance (d)=√5units
⇒d2=5