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AP EAMCET · Maths · Circle

If \(3 x+y+k=0\) is a tangent to the circle \(x^2+y^2=10\), then \(k=\ldots . . .\).

  1. A \pm 7
  2. B \pm 5
  3. C \pm 9
  4. D \pm 10
Verified Solution

Answer & Solution

Correct Answer

(B) \pm 5

Step-by-step Solution

Detailed explanation

Length of perpendicular from \((0,0)\) on \(3 x+y+k=0\) \(=\) radius of circle. \(\Rightarrow\left|\frac{3 \times 0+0+k}{\sqrt{3^2+12}}\right|=\sqrt{10} \Rightarrow \frac{k}{\sqrt{10}}= \pm \sqrt{10}\) \(\Rightarrow \quad k= \pm(\sqrt{10})^2 \Rightarrow k= \pm 10\)