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Find the co-ordinates of the points on the curve y=x-(4/x) where the tangents are parallel to the line y=2x - Mathematics and Statistics

Find the co-ordinates of the points on the curve y=x-(4/x) where the tangents are parallel to the line y=2x

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Solution

`y=x-4/x ... (1)`

Differentiat ing w.r.t. x,

`dy/dx=1+4/x^2`

`|dy/dx|_(x_1,y_1) =1+4/x_1^2=m`

Slope of the tangent , `m=1+4/x_1^2`

Also Slope of the line y= 2x, m1=2

m is parallel to m1

`1+4/x_1^2=2`

`4/x_1^2=1`

`x_1^2=4`

`therefore x_1=2, x_2=-2 `

using eq (1)

`y_1=2-(4/2) = 0`

`y_2= -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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