Curve is y=x2−4. Minimum distance from origin is along the normal passing through origin. Consider a point on curve (h,h2−4) Slope of tangent is 2x=2h at (h,h2−4) ∴ Slope of normal is −
1
2h
. ∴ Equation of normal is (y−(h2−4)=−‌
1
2h
(x−h)) This passes through (0,0). ∴−h2+4=
1
2
⇒h=±√
7
2
∴ Points on the curve at minimum distance from origin can be (±√