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AP EAMCET · Maths · Circle

The lengths of the intercepts made by a circle \(\mathrm{S}\) on \(\mathrm{X}\) and \(\mathrm{Y}\) - axes are \(\frac{2 \sqrt{13}}{3}\) and \(\frac{2 \sqrt{22}}{3}\) respectively. If the radius of the circle \(\mathrm{S}\) is \(\frac{\sqrt{38}}{3}\) and its centre \(\mathrm{C}\) lies in the second quadrant, then \(\mathrm{C}=\)

  1. A \(\left(\frac{-5}{3}, \frac{4}{3}\right)\)
  2. B \(\left(\frac{-4}{3}, \frac{5}{3}\right)\)
  3. C \(\left(\frac{-6}{5}, \frac{7}{5}\right)\)
  4. D \(\left(\frac{-7}{5}, \frac{6}{5}\right)\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(\left(\frac{-4}{3}, \frac{5}{3}\right)\)

Step-by-step Solution

Detailed explanation

Let equation of the circle be \(x^2+y^2+2 g x+2 f y+c=0\) ... (i) Now length of intercepts made by \(\mathrm{x}\) axis is \(2 \sqrt{\mathrm{g}^2-\mathrm{c}}=\frac{2 \sqrt{13}}{3} \Rightarrow \mathrm{g}^2-\mathrm{c}=\frac{13}{9}\) ... (ii) Similarly,…