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  • Need solution for RD Sharma maths Class 12 Chapter 15 Tangents and Normals Exercise Very short Answers Question 12 textbook solution.

Need solution for RD Sharma maths Class 12 Chapter 15 Tangents and Normals Exercise Very short Answers Question 12 textbook solution.

Answers (1)

Answer : Equation of tangent, x+y=2

Hint: Use the equation of tangent,

         y-y_{1}=\frac{d y}{d x}\left(x-x_{1}\right)

Given : Here the curve,

             y=x^{2}-x+2  at the point where it crosses the y-axis.

We have to write the equation of the tangent.

Solution :

We know that,

When the curve passes through  y - axis, then the point on the curve is of the form (0,y)

Now,   y=x^{2}-x+2

Differentiating with respect to x,

             \frac{d y}{d x}=2 x-1

           Slope of tangent =\left(\frac{d y}{d x}\right)_{(0,2)}=2(0)-1

                                     =-1= m (say)

\therefore \quad\left(x_{1}, y_{1}\right)=(0,2)_{\text {and }} m=1

Equation of tangent,

\begin{aligned} & y-y_{1}=m\left(x-x_{1}\right) \\ \Rightarrow & y-2=-1(x-0) \\ \Rightarrow & x+y=2 \end{aligned}

Hence the required equation of tangent, x+y = 2.

 

               

 

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