Find the co-ordinates of the points on the curve y=x-(4/x) where the tangents are parallel to the line y=2x
`y=x-4/x ... (1)`
Differentiat ing w.r.t. x,
Slope of the tangent , `m=1+4/x_1^2`
Also Slope of the line y= 2x, m1=2
m is parallel to m1
`therefore x_1=2, x_2=-2 `
using eq (1)
`y_1=2-(4/2) = 0`
Co ordinates of the point of contact are (2,0) and (-2,0).
Concept: Conics - Tangents from a Point Outside Conics
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