Question

hey 'reality' please solve this .fast
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Answer 1

Answer:

( 1 , 2 )

Step-by-step explanation:

Given :

Equation of curve y² = 4 x

We are asked to find points nearest to the point ( 2 , 1 )

Now , writing the parametric of curve which is nearest to given point i.e ( t² , 2 t )

Finding distance between them by using distance formula :

s = √ ( t² - 2 )² + ( 2 t - 1 )²

Squaring on both side :

s² =  ( t² - 2 )² + ( 2 t - 1 )²

Diff. w.r.t. t we get :

2 s ( d s / d t ) = 2 ( t² - 2 ) ( 2 t ) + 2  ( 2 t - 1 ) ( 2 )

We have to keep distance minimum so ( d s / d t = 0 )

2 ( t² - 2 ) ( 2 t ) + 2  ( 2 t - 1 ) ( 2 ) = 0

= > 4 [ ( t² - 2 ) ( t ) + ( 2 t - 1 ) ] = 0

= >  ( t² - 2 ) ( t ) + ( 2 t - 1 ) = 0

= > t³ - 2 t + 2 t - 1 = 0

= > t³ - 1 = 0

= > t³ = 1

= > t = 1

Therefore , required points ( 1 , 2 ) which is nearest to point ( 2 , 1 ).