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  • Find the angle between the tangent from the point (3,4) to the circle <img alt="$x^{2}+y^{2}=16$" src="https://learn.careers360.com/latex-image/?%24x%5E%7B2%7D&plus;y%5E%7B2%7D%3D16

Find the angle between the tangent from the point (3,4)
to the circle $x^{2}+y^{2}=16$

Option: 1

2 \tan ^{-1} (\frac{4}{3})


Option: 2

\tan ^{-1} (\frac{4}{3})


Option: 3

\tan ^{-1} (\frac{5}{3})


Option: 4

2 \tan ^{-1} (\frac{5}{3})


Answers (1)

best_answer

 

 

Pair of Tangent -

Pair of Tangent 
\\ {\text { The angle between the pair of tangents from }\left(x_{1}, y_{1}\right) \text { to }} \\ {\text { the circle } x^{2}+y^{2}=a^{2} \text { is }} \\ \text{\;\;\;\;\;\;\;\;\;\;\;\;\;\;}{2 \tan ^{-1}\left(\frac{a}{\sqrt{S_{1}}}\right)\\ \text { where } S_{1}=x_{1}^{2}+y_{1}^{2}-a^{2}}

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$ The angle between the tangent from the point \\ $\begin{aligned}(3,4) \text { to the circle } x^{2}+y^{2} &=16 \text { is } \\ 2 \tan ^{-1}\left(\frac{a}{\sqrt{S_{1}}}\right) &=2 \tan ^{-1}\left(\frac{4}{\sqrt{9+16-16}}\right) \\ &=2 \tan ^{-1}\left(\frac{4}{3}\right) \end{aligned}$

Posted by

Sanket Gandhi

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