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TS EAMCET · Maths · Circle

If the angle between the pair of tangents drawn to the circle \(x^2+y^2-2 x+4 y+3=0\) from \((6,-5)\) is \(\theta\), then \(\tan \theta=\)

  1. A \(\frac{5}{8}\)
  2. B \(\frac{15}{8}\)
  3. C \(\frac{8}{15}\)
  4. D \(\frac{19}{8}\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(\frac{8}{15}\)

Step-by-step Solution

Detailed explanation

Equation of circle is \(x^2+y^2-2 x+4 y+3=0\) \(\therefore\) Length of \(P A=\sqrt{S_1}\) \(\begin{aligned} & =\sqrt{(6)^2+(-5)^2-2(6)+4(-5)+3} \\ & =\sqrt{56+25-12-20+3} \\ & =\sqrt{32}=4 \sqrt{2}\end{aligned}\) and radius, \(O A=\sqrt{(1)^2+(-2)^2-3}=\sqrt{1+4-3}=\sqrt{2}\)…