Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • Provide Solution For R.D.Sharma Maths Class 12 Chapter 15 Tangents and Normals Exercise 15.1 Question 16 Maths Textbook Solution.

Provide Solution For  R.D.Sharma Maths Class 12 Chapter 15 Tangents and Normals Exercise 15.1 Question 16 Maths Textbook Solution.

Answers (1)

Answer: The requried points are (3,2)

Hint:\text { The slope of the tangent is the limit of } \frac{\Delta y}{\Delta x} \text { as } \Delta x \text { approaches zero. }

Given:

\text { Equation of the curve is } y=x^{2}-4 x+5 \quad \rightarrow(1)

\text { Equation of the line is } 2 y+x=7 \quad \rightarrow(2)

Solution:\text { Differentiating eqn(1) with respect to } x

\therefore \frac{d}{d x}\left(\mathrm{x}^{n}\right)=n x^{n-1}, \frac{d}{d x}(\text { constant })=0

\frac{d y}{d x}=2 x^{2-1}-4

\frac{d y}{d x}=2 x-4

\text { Slope } \mathrm{m}_{1}=\frac{d y}{d x}=2 x-4 \quad \rightarrow(3)

\text { Differentiating eqn }(2) \text { with respect to } x

2 \frac{d y}{d x}+1=0

2 \frac{d y}{d x}=-1

\frac{d y}{d x}=\frac{-1}{2}

\text { Slope } \mathrm{m}_{2}=\frac{d y}{d x}=\frac{-1}{2}

\text { We have given that slope(1) and slope (2) are perpendicular to each other }

Hence,

\begin{aligned} &m_{1} \times m_{2}=-1 \\ &(2 x-4) \times\left(\frac{-1}{2}\right)=-1 \\ &(2 x)\left(\frac{-1}{2}\right)-(4)\left(\frac{-1}{2}\right)=-1 \end{aligned}

\begin{aligned} &-x+2=-1 \\ &x=2+1 \\ &x=3 \end{aligned}

\text { When put } x=3 \text { in eqn (1) } y=x^{2}-4 x+5

\begin{aligned} &y=(3)^{2}-4(3)+5 \\ &y=9-12+5 \\ &y=2 \end{aligned}

Thus the required points are (3,2)

 

Posted by

infoexpert21

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

When will CBSE Class 12 results 2025 be declared? Last two years' trends
anam-khan

CBSE Class 10, 12 board exams 2025 from April 7 to 11 for sports students
anam-khan

CBSE Class 12 history paper 2025 moderately difficult, tested students’ understanding

Latest Question