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  • 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

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