Circle And System Of Circles Question 301
Question: If the line $ lx+my=1 $ be a tangent to the circle $ x^{2}+y^{2}=a^{2} $ , then the locus of the point (l, m) is
[MNR 1978; RPET 1997]
Options:
A) A straight line
B) A Circle
C) A parabola
D) An ellipse
Show Answer
Answer:
Correct Answer: B
Solution:
If the line $ lx+my-1=0 $ touches the circle $ x^{2}+y^{2}=a^{2} $ , then applying the condition of tangency, we have $ \pm \frac{l.0+m.0-1}{\sqrt{l^{2}+m^{2}}}=a $
On squaring and simplifying, we get the required locus $ x^{2}+y^{2}=\frac{1}{a^{2}} $ .
Hence it is a circle.
BETA
