Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • Please Solve RD Sharma Class 12 Chapter15 Tangents and Normals Exercise Fill in the blanks Question 7 Maths Textbook Solution.

Please Solve RD Sharma Class 12 Chapter15 Tangents and Normals Exercise Fill in the blanks Question 7 Maths Textbook Solution.

Answers (1)

Answer:

                \frac{\pi}{2}

Hint:

First we need to find their point of intersection. So solve these given equations.

Given:

Given curves,

              y= x^{2}    and  x= y^{2}

To find:

We have to find the angle of intersection of the given curves at  \left ( 0,0 \right )

Solution:

Here      y= x^{2}                                                                                                                                                                 … (i)

                x= y^{2}                                                                                                                                                              … (ii)

From equation (i) and (ii), we get

\begin{array}{ll} \Rightarrow & x^{4}=x \\\\ \Rightarrow & x^3(x-1)=0 \end{array} 

Which gives   x= 0,x= 1

Therefore points of intersection of the curves are  \left ( 0,0 \right ) and \left ( 1,1 \right )

On differentiating equation (i) and (ii), we get

\Rightarrow \quad \frac{d y}{d x}=2 x

Similarly, 2 y \frac{d y}{d x}=1

\Rightarrow \quad \frac{d y}{d x}=\frac{1}{2 y}

To find the angle of intersection at \left ( 0,0 \right )

So, m_{1} slope of tangent to curve y= x^{2} at  \left ( 0,0 \right )

            = 2x= 0

So tangent is parallel to x- axis.

        m_{2} = slope of tangent to curve  x= y^{2}  at \left ( 0,0 \right )

            = \frac{1}{2y}  which is not defined.

So tangent is parallel to y- axis.

Now, one tangent is parallel to  x-axis and other is parallel to  y-axis.

Hence angle between tangents is right angle. i.e. \frac{\pi}{2}

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