Q. If $3x + y + k = 0$ is a tangent to the circle $x^{2} + y^{2} = 10$, the values of $k$ are
A) $\pm 7$
B) $\pm 5$
C) $\pm 10$
D) $\pm 9$
Explanation
(c)
Given lines is $y = - 3x - k$
And equation of circle is $x^{2} + y^{2} = 10$
Here, $a^{2} = 10,\ m = - 3,\ c = - k$
For tangency, $c^{2} = a^{2}\left( 1 + m^{2} \right)$
For tangency, $c^{2} = a^{2}(1 + m^{2})$
$\Rightarrow \ k^{2} = 10(1 + 9)\ \Rightarrow k = \pm 10$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.