Q77 / 180 · COMEDK 2020 · Mathematics

If $3 x+y+k=0$ is a tangent to the circle $x^{2}+y^{2}=10$, the values of $k$ are

  • A
    $\pm 5$
  • B
    $\pm 7$
  • C
    $\pm 9$
  • Correct answer
    D
    $\pm 10$

Solution

We have, $3 x+y+k=0$ is iargent to the circle $x^{2}+v^{2}=10 .$ So, distance of line $3 x+y+k=0$ from centre of the circle will he equal to the radius of circle. $$ \begin{aligned} &\therefore \quad \mid \frac{3(0)+(0)+K}{\sqrt{(3)^{2}+(1)^{2}} \mid}=\sqrt{10} \\ &\Rightarrow \quad \frac{K}{\sqrt{10}}=\pm \sqrt{10} \Rightarrow K=\pm 10 \end{aligned} $$

Hence, the correct answer is option: 'D'.

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