Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • The acute angle between the line    and the circle 

The acute angle between the line  \mathrm{ 3 x-4 y=5}  and the circle  \mathrm{ x^2+y^2-4 x+2 y-4=0}  is \mathrm{ \theta} , then the value of  \mathrm{ \sin \theta} is

Option: 1

\frac{2 \sqrt{2}}{3}


Option: 2

\frac{\sqrt{2}}{3}


Option: 3

\frac{1}{3}


Option: 4

\frac{2}{3}


Answers (1)

best_answer

We have, the circle with centre (2,-1) and radius =3 Perpendicular distance from centre on  \mathrm{3 x-4 y=5} is given by

\mathrm{ p=\left|\frac{6+4-5}{5}\right|=1 }
\mathrm{ \therefore \quad \sin \left(90^{\circ}-\theta\right)=\frac{1}{3}}

\mathrm{ \Rightarrow \cos \theta=1 / 3 \Rightarrow \sin \theta=\frac{2 \sqrt{2}}{3}}??????

Posted by

Sayak

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Trending Articles/News

anam-khan

BTech aspirant from north-east or UT? Apply for CSAB NEUT counselling 2025 today
anam-khan

JoSAA round 2 cut-off 2025 out; BTech closing ranks for top engineering courses at IITs
anam-khan

Goa Engineering Admission 2025: 1,415 eligible for BE seats; merit list on June 27

Latest Question