the line y=2x +c is tanget to parabola y^2=4x ,then the value of c is equal to
The line y = 2x + c will be tangential to the parabola y^2 = 4x at a common point, say (x0, y0).
The slope of the line is m = 2.
The slope of the parabola at the common point, (x0, y0), must also be dy/dx = m = 2
Differentiating y^2 = 4x, wrt x,
2y.y' = 4
y' = 2/y
dy/dx = 2/y
i.e. 2/y = m = 2
Therefore, y = y0 = 1
And x = x0 = 1/4 (using y^2 = 4x)
Using y = 2x + c, at the common point (x0, y0) = (1/4, 1), then
y0 = 2.x0 + c
1 = 1/2 + c
c = 1/2