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 Multiple Choice Questions Question 19 Maths Textbook Solution.

Provide Solution For  R.D. Sharma Maths Class 12 Chapter 15 Tangents and Normals Exercise Multiple Choice Questions Question 19 Maths Textbook Solution.

Answers (1)

Answer:

            (c) Is the correct option 

Hint:

        Equation of normal y-y_{1}=m\left ( x-x_{1} \right )

Given:

             x=a \cos ^{3} \theta, y=a \sin ^{3} \theta

Solution:

x=a \cos ^{3} \theta            (1)

Differentiating w.r.t \theta

\begin{aligned} &\frac{d x}{d \theta}=a \cdot 3 \cos ^{2} \theta(-\sin \theta) \\ &=-3 a \cos ^{2} \theta \sin \theta \\ &\left.\frac{d x}{d \theta}\right|_{\theta-\frac{\pi}{4}}=-3 a \times \frac{1}{2} \times \frac{1}{\sqrt{2}}=-\frac{3 a}{2 \sqrt{2}} \\ &y=a \sin ^{3} \theta \end{aligned}

Differentiating w.r.t \theta

\begin{aligned} &\frac{d y}{d \theta}=a \times 3 \sin ^{2} \theta \cos \theta \\ &\left.\frac{d y}{d \theta}\right|_{\theta-\frac{\pi}{4}}=3 a \times \frac{1}{2} \times \frac{1}{\sqrt{2}}=\frac{3 a}{2 \sqrt{2}} \end{aligned}

Slope of normal of the given curve M(N)=-\frac{d x}{d y}=-\left(\frac{\frac{d x}{d \theta}}{\frac{d y}{d \theta}}\right)=-\left(\frac{\frac{3 \alpha}{2 \sqrt{2}}}{\frac{-3 \alpha}{2 \sqrt{2}}}\right)=1

Equation of normal at \theta =\frac{\pi }{4}

\begin{aligned} &y-\frac{a}{(\sqrt{2})^{3}}=1\left(x-\left(\frac{a}{\sqrt{2}}\right)^{3}\right) \\ &y=x \end{aligned}

 

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

CBSE Class 10, 12 compartment 2024 exams today for 2.5 lakh students; exam timings, guidelines
anam-khan

CBSE compartment admit card 2024 out at cbse.gov.in; exams from July 15
anam-khan

Reports saying CBSE cannot conduct board exams twice a year currently ‘totally incorrect’; board denies claims

Latest Question