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  • Need solution for RD Sharm Maths Class 12 Chapter 15 Tangents and Normals Excercise Fill in the blanks Question 20

Need solution for RD Sharm Maths Class 12 Chapter 15 Tangents and Normals Excercise Fill in the blanks Question 20

Answers (1)

Answer:

                y=0  is the required equation of normal

Hint:

Equation of normal,

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

Given:

Given curve,

                y^{2}=8x

To find:

We have to find the equation of normal to the given curve at the origin.

Solution:

We have,

                y^{2}=8x

On differentiating both side with respect to x , we get

\Rightarrow 2 y \frac{d y}{d x}=8                                                                                                                         \left[\because \frac{d\left(x^{n}\right)}{d x}=n x^{n-1}\right]

\begin{aligned} &\Rightarrow \frac{d y}{d x}=\frac{8}{2 y} \\ &\Rightarrow \frac{d y}{d x}=\frac{4}{y} \\ &\Rightarrow-\left(\frac{d x}{d y}\right)=\frac{-y}{4} \end{aligned}

At origin i.e. \left ( 0,0 \right )

Here the equation of normal,

\begin{aligned} &\left(y-y_{1}\right)=-\left(\frac{d x}{d y}\right)_{(0.0)}\left(x-x_{1}\right) \\ \Rightarrow \quad &(y-0)=0(x-0) \\ \Rightarrow \quad & y=0 \end{aligned}

Hence the required equation of normal is y=0.

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