Find the coordinates of the point on the curve `y=x-(4)/(x)`, where the tangent is parallel to the line `y=2x`.

Explanation

Equation of line is given by
` y = 2x ` ….(1)
We know that
` y = mx + c ` …(2)
On comparing equation (2) with (1),
We get ,
m = 2
Given, ` y = x - 4/x`
Differentiating w.r.t.x
` (dy)/(dx) = 1 - 4 (-1) * 1/x^(2) `
` = 1 + 4/x^(2) = m ` ....(3)
Slope of the tangent, ` m = 1 + 4/x^(2) `
` 1 + 4/x^(2) = 2`
` x^(2) + 4 = 2x^(2)`
` x = pm 2`
` :. x_(1) = 2, x_(2) = -2`
` y_(1) = 4, y_(2) = - 4`
Co- ordinates of the point of contact are (2, 4) and (-2, -4).