The shortest distance between the point 3 2 , 0 and the curve y = x , x > 0 , is

Step-by-step solution

Let P be the nearest to 3 2 ,   0 , then normal at P will pass through 3 2 ,   0 . Any point on the parabola y 2 = 4 a x can be taken as a t 2 ,   2 a t Let, co-ordinates of P on the curve y = x ,   ⇒ y 2 = x can be taken as t 2 4 ,   t 2 The equation of the normal to the parabola y 2 = 4 a x at a point a t 2 ,   2 a t is y + t x = 2 a t + a t 3 . Hence, the equation of normal to y = x or y 2 = x at t 2 4 ,   t 2 is y + t x = t 2 + t 3 4 This line passes through 3 2 ,