Find the equations of all lines having slope 2 which are tangent to the curve y = 1/(x - 3), x ≠ 3

Solution:

For a curve y = f(x) containing the point (x₁,y₁) the equation of the tangent line to the curve at (x₁,y₁) is given by 

y − y₁ = f′(x₁) (x − x₁)

The slope of a line is nothing but the change in y coordinate with respect to the change in x coordinate of that line.

The given curve is y

= 1 / (x - 3)

The slope of the tangents to the given curve is given by,

dy/dx

= d/dx 1/(x - 3)

- 1 / (x - 3)²

The slope of the tangent is 2.

So, we have:

- 1 / (x - 3)² = 2

⇒ 2 (x - 3)² = - 1

⇒ (x - 3)² 

= - 1/2

It is not possible since the LHS is positive and RHS is negative.

Thus, there is no tangent to the curve of slope 2

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NCERT Solutions Class 12 Maths - Chapter 6 Exercise 6.3 Question 11

Find the equations of all lines having slope 2 which are tangent to the curve y = 1/(x - 3), x ≠ 3.

Summary:

There is no equation possible for all lines having slope 2 which are tangent to the curve y = 1/(x - 3), x ≠ 3