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AP EAMCET · Maths · Circle

If the line \(3 x-4 y=1\) touches the circle \((x-1)^2+(y+2)^2=4\) at \((\alpha, \beta)\), the values of \(\alpha\) and \(\beta\) are

  1. A \(\alpha=\frac{1}{5}, \beta=-\frac{1}{10}\)
  2. B \(\alpha=\frac{-1}{5}, \beta=-\frac{2}{5}\)
  3. C \(\alpha=\frac{-2}{5}, \beta=\frac{-11}{20}\)
  4. D \(\alpha=\frac{2}{5}, \beta=\frac{1}{20}\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(\alpha=\frac{-1}{5}, \beta=-\frac{2}{5}\)

Step-by-step Solution

Detailed explanation

\((\alpha, \beta)\) lies on the line \(3 x-4 y=1\) \[ \begin{array}{r} 3 \alpha-4 \beta=1 \\ \Rightarrow \quad \beta=\frac{(3 \alpha-1)}{4} \end{array} \] \((\alpha, \beta)\) also lie on the circle…