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  • The angle between pair of tangents to the curve  from the

The angle between pair of tangents to the curve \mathrm{9 x^2-25 y^2=225} from the point \mathrm{M(2 \sqrt{2}, 2 \sqrt{2})} is

Option: 1

\mathrm{2 \tan ^{-1} \frac{1}{2}}


Option: 2

\mathrm{2 \tan ^{-1} 2}


Option: 3

\mathrm{2\left(\tan ^{-1} \frac{1}{3}+\tan ^{-1} \frac{1}{2}\right)}


Option: 4

\mathrm{2 \tan ^{-1} 3}


Answers (1)

best_answer

The equation of the director circle of the given hyperbola is x^2+y^2=25-9 \Rightarrow x^2+y^2=16

Clearly, the point M(2 \sqrt{2}, 2 \sqrt{2}) lies on the director circle

x^2+y^2=16.
So, the angle between the tangents to the hyperbola drawn

from M(2 \sqrt{2}, 2 \sqrt{2}) is a right angle.

Now,2\left(\tan ^{-1} \frac{1}{3}+\tan ^{-1} \frac{1}{2}\right)=2 \tan ^{-1}\left(\frac{\frac{1}{3}+\frac{1}{2}}{1-\frac{1}{3} \times \frac{1}{2}}\right)=2 \tan ^{-1} 1=\frac{\pi}{2}

Posted by

Rishabh

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