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Explain solution for RD Sharma maths Class 12 Chapter 15 Tangents and Normals Exercise Multiple Choice Question, Question 34 maths textbook solution.

Answers (1)

Answer : (a) is the correct option

Hint :

      Equation of tangent y-y_{1}=m\left(x-x_{1}\right)

Given :


Solution :

y\left(1+x^{2}\right)=2-x                                            (1)

Since it crosses x -axis

\begin{aligned} &2-x=0 \\ &x=2 \end{aligned}

The point of contact (2,0)

Differentiating (1) w.r.t x

\begin{aligned} &y(2 x)+\left(1+x^{2}\right) \frac{d y}{d x}=-1 \\ &\text { At }(2,0) \\ &0(2 \times 2)+\left(1+2^{2}\right) \frac{d y}{d x}=-1 \\ &\frac{d y}{d x}=-\frac{1}{5} \end{aligned}

Equation of tangent at (1,2)

\begin{aligned} &y-0=-\frac{1}{5}(x-2) \\ &5 y=-x+2 \\ &x+5 y=2 \end{aligned}

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