Angle between pair of tangents from the point (1, 1/2) to circle x^2 + y^2 + 4x + 2y -4=0 is-

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10-1.Circle and System of Circles

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The angle between the pair of tangents from the point $(1, 1/2)$ to the circle $x^2 + y^2 + 4x + 2y -4=0$ is-

A

${\cos ^{ - 1}}\frac{4}{5}$

B

${\sin ^{ - 1}}\frac{4}{5}$

C

${\sin ^{ - 1}}\frac{3}{5}$

D

None of these

Solution

$\mathrm{r}=3$

$\sqrt{S_{1}}=\frac{3}{2}$

$ 2 \propto =2 \tan ^{-1}\left(\frac{r}{\sqrt{S_{1}}}\right) $

$=2 \tan ^{-1}\left(\frac{3}{3 / 2}\right)=2 \tan ^{-1}(2)=\sin ^{-1}\left(\frac{4}{5}\right)$

Standard 11

Mathematics

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(JEE MAIN-2019)