Circle And System Of Circles Question 307
Question: 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
Options:
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
Show Answer
Answer:
Correct Answer: A
Solution:
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 $ | \frac{k}{\sqrt{1+3}} |=a\Rightarrow k=\pm 2a $
Hence the required equation is $ \sqrt{3}x+y\pm 2a=0. $
BETA
