The minimum distance of a point on the curve y = x 2 - 4 from the origin is

Step-by-step solution

A variable point on the given parabola can be taken as α ,   α 2 - 4 Distance from origin D =   α 2 + α 2 - 4 2 ⇒ D 2 = α 2 + α 4 + 16 - 8 α 2 = α 4 - 7 α 2 + 16 d D 2 d α = 4 α 3 - 14   α = 0 ⇒ 2 α 2 α 2 - 7 = 0 ⇒   α = 0 ,   7 2 ,   - 7 2 ∴   D m i n   2   a t   α 2 = 7 2 D m i n 2 = 49 4 - 49 2 + 16 =   - 49 4 + 16 = 15 4 D m i n = 15 2