The line `y = m x + 1`is a tangent to the curve `y^2=4x`if the value of m is

Options

A. 1
B. 2
C. 3
D. `1/2`

Answer

A

Explanation

Equation of tangent on the curve is `y=mx+1`.
`:." Given curve "y^(2)=4x`
` rArr 2y(dy)/(dx) = 4 rArr (dy)/(dx) = 2/y`
If the tangent of the curve is `y=mx + 1" then "2/y = m`
` rArr y = 2/m`
put the value of y in equation (1),
` x = y^(2)/4 = 1/4 (2/m)^(2) = 1/m^(2)`
`:. ` The point will satisfy the line `y=mx + 1`
`:. 2/m = m(1/m^(2))+1 rArr 1/m = 1 rArr m = 1`