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  • The angle between the tangents drawn from the point to the parabola<img alt="\mathrm{ y^2=4 x}" src="https://en

The angle between the tangents drawn from the point (1,4) to the parabola\mathrm{ y^2=4 x} is
 

Option: 1

\mathrm{\frac{\pi}{6}}
 


Option: 2

\mathrm{\frac{\pi}{4}}
 


Option: 3

\mathrm{\frac{\pi}{3}}
 


Option: 4

\mathrm{\frac{\pi}{2}}


Answers (1)

best_answer

Equation of tangent is \mathrm{y=m x+\frac{1}{m}} Since it passes through \mathrm{(1,4)}

\mathrm{ \therefore \quad m^2-4 m+1=0 \Rightarrow m_1+m_2=4, m_1 m_2=1 }

\mathrm{\Rightarrow\left|m_1-m_2\right|=2 \sqrt{3}, \tan \theta=\left|\frac{m_1-m_2}{1+m_1 m_2}\right| }

\mathrm{ \therefore \tan \theta=\frac{2 \sqrt{3}}{2}=\sqrt{3} \quad \therefore \theta=\frac{\pi}{3} }

Hence option 3 is correct.




 

Posted by

Divya Prakash Singh

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