Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • Need solution for RD Sharma Maths Class 12 Chapter 15 Tangents and Normals Excercise Fill in the blanks Question 17

Need solution for RD Sharma Maths Class 12 Chapter 15 Tangents and Normals Excercise Fill in the blanks Question 17

Answers (1)

Answer:

Equation of normal,  y=3x-5

Hint:

Use equation of normal,

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

Given:

Given curve,

                x^{2}+y^{2}-2 x+4 y-5=0

To find:

We have to find the slope of normal to the given curve at point  \left ( 2,1 \right )

Solution:

Given equation is

                x^{2}+y^{2}-2 x+4 y-5=0

On differentiating both side with respect to x , we get

\Rightarrow \quad 2 x+2 y \frac{d y}{d x}-2+4 \frac{d y}{d x}=0                                                                                         \left[\because \frac{d\left(x^{n}\right)}{d x}=n x^{n-1}\right]

\Rightarrow \quad(y+2) \frac{d y}{d x}=1-x     [Taking common 2  from each term]

\begin{aligned} &\Rightarrow \quad \frac{d y}{d x}=\frac{1-x}{y+2} \\\\ &\Rightarrow \quad\left(\frac{d y}{d x}\right)_{(2,1)}=\frac{1-2}{1+2}=\frac{-1}{3} \\ \end{aligned}

\Rightarrow \quad-\left(\frac{d y}{d x}\right)_{(2,1)}=\frac{1}{3}

\Rightarrow \quad-\left(\frac{d x}{d y}\right)_{(2,1)}=3

Now, equation of normal is

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

Substituting these value, we get

           i.e.   y_{1}=1, x_{1}=2, \frac{-d x}{d y}=3

             \begin{aligned} &(y-1)=3(x-2) \\ \Rightarrow & \quad y-1=3 x-6 \\ \Rightarrow & \quad y=3 x-5 \end{aligned}

Hence, y=3 x-5 is required equation of normal.

Posted by

infoexpert27

View full answer

Crack CUET with india's "Best Teachers"

  • HD Video Lectures
  • Unlimited Mock Tests
  • Faculty Support
cuet_ads

Similar Questions

Trending Articles/News

anam-khan

CBSE Single Girl Child Scholarship 2024: Registration extended till January 10; eligibility criteria, amount
anam-khan

CBSE wants international boards reined in; letter to education ministry seeks directions for AIU
anam-khan

PM Modi's Pariksha Pe Charcha 2025 to be held next month, registrations open till January 14

Latest Question