HSC Science (Computer Science) 12th Board ExamMaharashtra State Board
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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 - HSC Science (Computer Science) 12th Board Exam - Mathematics and Statistics

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ConceptConics Tangents from a Point Outside Conics

#### Question

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

#### 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).

Is there an error in this question or solution?

#### APPEARS IN

2014-2015 (March) (with solutions)
Question 5.2.1 | 4.00 marks
Solution Find the co-ordinates of the points on the curve y=x-(4/x) where the tangents are parallel to the line y=2x Concept: Conics - Tangents from a Point Outside Conics.
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