Let the point (h,k) lie on the curve x2=2y. ∴h2=2k D=√h2+(k−5)2 ⇒D=√2k+k2−10k+25[∵h2=2k] ⇒D=√k2−8k+25 ⇒D2=k2−8k+25 ⇒z=k2−8k+25[ let, D2=z] ⇒
dz
dk
=2k−8 For maxima or minima put,
dz
dk
=0 ⇒2k−8=0⇒k=4 and h=2√2 Now,
d2z
dk2
=2>0 ∴ Distance is minimum at (h,k)=(2√2,4) D=√k2−8k+25 D=√16−32+25=9=3