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  • The angle between the pair of tangents from the point (1,2) to the ellipse <img alt="\mathrm{3 x^2+2 y^2=5}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7B3%20x%5E2&plus

The angle between the pair of tangents from the point (1,2) to the ellipse \mathrm{3 x^2+2 y^2=5} is

Option: 1

\tan ^{-1}\left(\frac{12}{5}\right)


Option: 2

\tan ^{-1}\left(\frac{6}{\sqrt{5}}\right)


Option: 3

\tan ^{-1}\left(\frac{12}{\sqrt{5}}\right)


Option: 4

\tan ^{-1}(12 \sqrt{5})


Answers (1)

best_answer

The combined equation of the pair of tangents drawn from (1, 2) to the ellipse\mathrm{3 x^2+2 y^2=5} is

\mathrm{\begin{aligned} & \left(3 x^2+2 y^2-5\right)(3+8-5)=(3 x+4 y-5)^2\left[\mathrm{Using} S S^{\prime}=T^2\right] \\ & \because 9 x^2-24 x y-4 y^2+30 x+40 y-55=0 \end{aligned}}

\mathrm{\text { If angle between these lines is } \theta \text {, then } \tan \theta=\frac{2 \sqrt{h^2-a b}}{a+b} \text {, }}

where a = 9, h = –12, b = –4

\mathrm{\Rightarrow \tan \theta=\frac{12}{\sqrt{5}} \Rightarrow \theta=\tan ^{-1}\left(\frac{12}{\sqrt{5}}\right)}

 

Posted by

vishal kumar

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