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 \(\tan \theta=\)
- A \(\frac{5}{8}\)
- B \(\frac{15}{8}\)
- C \(\frac{8}{15}\)
- D \(\frac{19}{8}\)
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, \(O A=\sqrt{(1)^2+(-2)^2-3}=\sqrt{1+4-3}=\sqrt{2}\)…
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