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

Option: 1

\mathrm{\tan ^{-1}(12 / 5)}


Option: 2

\mathrm{\tan ^{-1}(6 / \sqrt{5})}


Option: 3

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


Option: 4

\mathrm{\tan ^{-1}(6 / 5)}


Answers (1)

best_answer

The combined equation of the pair of tangents drawn from \left ( 1,2 \right ) to the ellipse \mathrm{3 x^2+2 y^2=5} is
\mathrm{\left(3 x^2+2 y^2-5\right)(3+8-5)=(3 x+4 y-5)^2} \mathrm{\text { [using } S S_1=T^2 \text { ] }}
\mathrm{\Rightarrow 9 x^2-24 x y-4 y^2+\ldots \ldots=0}
The angle between the lines given by this equation is \mathrm{\tan \theta=\frac{2 \sqrt{h^2-a b}}{a+b}}
\mathrm{\text { Where } a=9, h=-12, \quad b=-4 \Rightarrow \tan \theta=12 / \sqrt{5} \Rightarrow \theta=\tan ^{-1}(12 / \sqrt{5})}

Posted by

Pankaj Sanodiya

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