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  • The angle between the tangents drawn from to the circle <img alt="\mathrm{x^2+y^2=10}" src="https://entrancecor

The angle between the tangents drawn from (4,2) to the circle \mathrm{x^2+y^2=10} is equal to
 

Option: 1

\frac{\pi}{3}
 


Option: 2

\frac{\pi}{4}

 


Option: 3

\frac{\pi}{6}
 


Option: 4

\frac{\pi}{2}


Answers (1)

best_answer

Equations of tangents to the circle may be written as

\mathrm{ y=m x \pm \sqrt{10\left(1+m^2\right)} }

Since these passes through \mathrm{ (4,2) }

\mathrm{ \Rightarrow 6 m^2-16 m-6=0 \Rightarrow m_1 m_2=-1 }

Hence option 4 is correct.
 

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