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 Exercise Very short Answers Question 11 textbook solution.

Need solution for RD Sharma maths Class 12 Chapter 15 Tangents and Normals Exercise Very short Answers Question 11 textbook solution.

Answers (1)

Answer : \left(x_{1}, y_{1}\right)=\left(\frac{1}{2}, 1\right)

Hint :

For line, the slope of a line is denoted by m.

               y=m x+c, where m is slope of line.

Given :

Given that the curve, y^{2}=3-4 x

Where the tangent parallel to the line, 2 x+y-2=0

We have to find the co-ordinate of the point on the given curve.

Solution :

Let \left(x_{1}, y_{1}\right) be the required point

We know that,

If  2 x+y-2=0

\Rightarrow \quad y=-2 x+2

Comparing with equation:

y=mx+c

We get, m=-2

Slope of the given line =-2

Since, the point lies on the curve

So         y_{1}^{2}=3-4x_{1}                                                                                      ...(i)

Now,      y^{2}=3-4x

Differentiate with respect to x

\begin{array}{ll} \Rightarrow \quad & 2 y \frac{d y}{d x}=-4 \\ \therefore & \frac{d y}{d x}=\frac{-2}{y} \end{array}

             Slope of tangent =\left(\frac{d y}{d x}\right)_{\left(x_{1}, y_{1}\right)}=\frac{-2}{y_{1}}

Here,     slope of tangent=slope of the line

\begin{aligned} &\Rightarrow \quad \frac{-2}{y_{1}}=-2 \\ &\Rightarrow \quad y_{1}=1 \end{aligned}

From equation (i), we get

\begin{aligned} & 1=3-4 x_{1} \\ \Rightarrow & 4 x_{1}=2 \\ \Rightarrow & x_{1}=\frac{1}{2} \end{aligned}

Hence, \left(x_{1}, y_{1}\right)=\left(\frac{1}{2}, 1\right)

 

 

 

 

Posted by

infoexpert23

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

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

CBSE Board Exams 2025: Online portal for availing exemptions by CWSN students opens
anam-khan

Board Exams: States agree to equivalence; no question paper ‘jumbling’ from next year, says PARAKH CEO

Latest Question