Solve this : 6 Find the point on the curve y2 = 4x which is nearest to - Maths - Application of Derivatives

Question

Solve this :

6 Find the point on the curve y2 = 4x
which is nearest to the point (2, 1)

Lovina Kansal · Accepted Answer

Dear student

Let (h,k) be any point on the curve y2=4xSo, (h,k) satisfies the equation y2=4xi
e k2=4h⇒h=k24Now, distance between (h,k) and (2,1) isD=h-22+(k-1)2    Distance formula between two points⇒D=k24-22+(k-1)2⇒D2=k24-22+(k-1)2Differentaite it w
r t k
, we het2DdDdk=2k24-2×ddkk24-2+2(k-1)×ddk(k-1)⇒2DdDdk=2k24-2k2+2(k-1)⇒DdDdk=k24-2k2+(k-1)⇒dDdk=1Dk24-2k2+(k-1)For the required point to be nearest to the point (2,1) distance D should be minimum i
e dDdk=0So,1Dk24-2k2+(k-1)=0⇒k24-2k2+(k-1)=0⇒k-1=0 or k24-2k2=0⇒k=1 or k24-2=0⇒k=1 or k=22So, When k=1, then h=14When k=22,then h=2224=2So, Required points are 14,1 or 2,22

Solve this : 6. Find the point on the curve y2 = 4x which is nearest to the point (2, 1).

Solve this :

6. Find the point on the curve y² = 4x which is nearest to the point (2, 1).