#### Need Solution for R.D.Sharma Maths Class 12 Chapter 15 Tangents and Normals Exercise Multiple Choice Question Question 11 Maths Textbook Solution.

$\left ( b \right )x+y-1=x-y-2$

Hint:

Use slope of the tangent $m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

Given:

$y=x^{2}-3x+2$

Solution:

$y=x^{2}-3x+2$

Let the tangent meet the x-axis at point $\left ( x,o \right )$

$\frac{dy}{dx}=2x-3$

The tangent passes through point $\left ( x,o \right )$

\begin{aligned} &0=x^{2}-3 x+2 \\ &(x-2)(x-1)=0 \\ &\Rightarrow x=2, x=1 \end{aligned}

Case 1

When $x=2$

Slope of tangent $\frac{dy}{dx}|\left ( _{2,0} \right )=2\left ( 2 \right )-3=4-3=1$

$\therefore \left ( x_{1},y_{1} \right )=\left ( 2,0 \right )$

Equation of tangent

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

Case 2

When $x=1$

Slope of tangent

$\frac{dy}{dx}|\left ( 2,0 \right )=2-3=-1$

$\left ( x_{1}-y_{1} \right )=\left ( 1,0 \right )$

Equation of tangent

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