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  • Need solution for RD Sharma Maths Class 12 Chapter 15 Tangents and Normals Excercise Fill in the blanks Question 11

Need solution for RD Sharma Maths Class 12 Chapter 15 Tangents and Normals Excercise Fill in the blanks Question 11

Answers (1)

Answer:

                a+b= 10

Hint:

First find the equation of normal then comparing with a x-b y+b=0

Given:

The given equation of curve,

             y^{2}=5 x-1  

To find:

We have to find the value of  a+b

Solution:

We have,

                y^{2}=5 x-1                                                                                                                              … (i)

Differentiating equation (i) with respect to x , we get

\Rightarrow \quad 2 y \frac{d y}{d x}=5                                                                                                                        \left[\because \frac{d\left(x^{n}\right)}{d x}=n x^{n-1}\right]

\begin{aligned} &\Rightarrow \quad \frac{d y}{d x}=\frac{5}{2 y} \\\\ &\therefore \quad\left(\frac{d y}{d x}\right)_{(1,-2)}=\frac{-5}{4} \end{aligned}

Then the equation of normal at point \left ( 1,-2 \right )  is

 \begin{array}{ll} & (y-(-2))=\frac{-1}{\frac{-5}{4}}(x-1) \\\\ \Rightarrow \quad & 5(y+2)=4(x-1) \\\\ \Rightarrow \quad & 4 x-5 y-14=0 \end{array}                                                                                                                       … (ii)

As the normal is of the form  a x-5 y+b=0                                                                                      … (iii)

Comparing equation (ii) and (iii), we get

               a= 4   and b= -14

Hence   a+b=-10

 

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