ExamBro
ExamBro
AP EAMCET · Maths · Circle

The angle between the tangents drawn from a point \((4,3)\) to the circle \(x^2+y^2-2 x-4 y=0\) is

  1. A \(\frac{\pi}{6}\)
  2. B \(\frac{\pi}{4}\)
  3. C \(\frac{\pi}{3}\)
  4. D \(\frac{\pi}{2}\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(\frac{\pi}{2}\)

Step-by-step Solution

Detailed explanation

Center \(C=(1,2)\), radius \(r=\sqrt{1^2+2^2-0}=\sqrt{5}\). Distance \(d=\sqrt{(4-1)^2+(3-2)^2}=\sqrt{3^2+1^2}=\sqrt{10}\). \(\sin\theta = \frac{r}{d} = \frac{\sqrt{5}}{\sqrt{10}} = \frac{1}{\sqrt{2}}\). \(\theta = \frac{\pi}{4}\). Angle between tangents…