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TS EAMCET · Maths · Circle

If the line \(x+3 y=0\) is the tangent at \((0,0)\) to the circle of radius 1 , then the centre of one such circle is

  1. A \((3,0)\)
  2. B \(\left(\frac{-1}{\sqrt{10}}, \frac{3}{\sqrt{10}}\right)\)
  3. C \(\left(\frac{3}{\sqrt{10}}, \frac{-3}{\sqrt{10}}\right)\)
  4. D \(\left(\frac{1}{\sqrt{10}}, \frac{3}{\sqrt{10}}\right)\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(\left(\frac{1}{\sqrt{10}}, \frac{3}{\sqrt{10}}\right)\)

Step-by-step Solution

Detailed explanation

Given line is \(x+3 y=0\). \(\therefore\) Slope of a line \(=-\frac{1}{3}\) Let the centres of circle be \((+g,+f)\). We know that, the perpendicular drawn from the centre to the tangent is equal to radius. Since perpendicular distance from \((g, f)\) to the line is 1 . Since…