Question

find the point on the curve y2=4x,the tangent at which is parallel to the straight line y=2x+4​

Answer 1

2ydy/dx=4

dy/dx=4/y

dy/dx=2

4/y=2

4=2y

y=2

substitute in equation

y=2(2)+4=8

x=1

point(x,y)=(1,8)

Answer 2

Step-by-step explanation: tangent are parallel to line means slopes are equal ,  given curve  y² = 4x   ------------ (1) and equation of straight line y = 2x +4 ---------------- (2)     now differentating  (1) with respect to x

2y dy/dx  = 4

dy/dx    = 2/y               and slope of line = - cofficient of x / coffcient of y

                                                                   = - (-2)/1

                                                                   = 2

now    2/y  = 2      ( tangent are parallel , slopes are equal)

           y = 1      put in first we get x = 1/4    so point are  ( 1/4 , 1)