Circle And System Of Circles Question 334
Question: Two tangents drawn from the origin to the circle $ x^{2}+y^{2}+2gx+2fy+c=0 $ will be perpendicular to each other, if
Options:
A) $ g^{2}+f^{2}=2c $
B) $ g=f=c^{2} $
C) $ g+f=c $
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
The equation of tangents will be $ c(x^{2}+y^{2}+2gx+2fy+c)={{(gx+fy+c)}^{2}} $ These tangents are perpendicular,
Hence the coefficients of $ x^{2} $ + coefficients of $ y^{2}=0 $
$ \Rightarrow c-g^{2}+c-f^{2}=0\Rightarrow f^{2}+g^{2}=2c $ .
BETA
