AP EAMCET · Maths · Circle
If \(\theta\) is the angle between the tangents drawn from the point \((2,3)\) to the circle \(x^2+y^2-6 x+4 y+12=0\), then \(\theta=\)
- A \(\cos ^{-1}\left(\frac{5}{13}\right)\)
- B \(\sin ^{-1}\left(\frac{4}{5}\right)\)
- C \(2 \tan ^{-1}\left(\frac{5}{12}\right)\)
- D \(\tan ^{-1}\left(\frac{5}{12}\right)\)
Answer & Solution
Correct Answer
(D) \(\tan ^{-1}\left(\frac{5}{12}\right)\)
Step-by-step Solution
Detailed explanation
Given the equation of circle \(\begin{aligned}& x^2+y^2-6 x+4 y+12=0 \\& \Rightarrow(x-3)^2+(y+2)^2=1\end{aligned}\) Since, \(A O=\sqrt{(3-2)^2+(-2-3)^2}=\sqrt{1+25}=\sqrt{26}\) and, \(A P=\sqrt{26-1}=5\) Now, in…
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