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AP EAMCET · Maths · Circle

The angle between the tangents drawn from the origin to the circle \(x^2+y^2+4 x-6 y+4=0\) is

  1. A \(\tan ^{-1}\left(\frac{5}{13}\right)\)
  2. B \(\tan ^{-1}\left(\frac{5}{12}\right)\)
  3. C \(\tan ^{-1}\left(\frac{-12}{2}\right)\)
  4. D \(\tan ^{-1}\left(\frac{13}{2}\right)\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(\tan ^{-1}\left(\frac{-12}{2}\right)\)

Step-by-step Solution

Detailed explanation

We have, \(x^2+y^2+4 x-6 y+4=0\) \(\text { Centre } \equiv(-g,-f) \equiv(-2,3)\) Radius of circle, \(\mathrm{OA}=\sqrt{g^2+f^2-c}\) \(\begin{aligned} & =\sqrt{(2)^2+(-3)^2-4} \\ & =\sqrt{4+9-4}=3 \end{aligned}\) Length of tangent…