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10-1.Circle and System of Circles
medium
The equations of the tangents to the circle ${x^2} + {y^2} = {a^2}$ parallel to the line $\sqrt 3 x + y + 3 = 0$ are
A
$\sqrt 3 x + y \pm 2a = 0$
B
$\sqrt 3 x + y \pm a = 0$
C
$\sqrt 3 x + y \pm 4a = 0$
D
None of these
Solution
(a) Equation of line parallel to the $\sqrt 3 x + y + 3 = 0$ is
$\sqrt 3 x + y + k = 0$…..$(i)$
But it is a tangent to the circle ${x^2} + {y^2} = {a^2}$, then
$\left| {\frac{k}{{\sqrt {1 + 3} }}} \right| = a $
$\Rightarrow k = \pm 2a$
Hence the required equation is $\sqrt 3 x + y \pm 2a = 0.$
Standard 11
Mathematics
