Circle And System Of Circles Question 351
Question: The distance between the chords of contact of the tangents to the circle $ x^{2}+y^{2}+2gx+2fy+c=0 $ from the origin and the point $ (g,f) $ is
Options:
A) $ \frac{1}{2}( \frac{g^{2}+f^{2}-c}{\sqrt{g^{2}+f^{2}}} ) $
B) $ ( \frac{g^{2}+f^{2}-c}{\sqrt{g^{2}+f^{2}}} ) $
C) $ \frac{1}{2}( \frac{g^{2}+f^{2}-c}{g^{2}+f^{2}} ) $
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
Chord of contact from origin $ \equiv gx+fy+c=0 $ and from $ (g,\ f)\equiv gx+fy+g(x+g)+f(y+f)+c=0 $ or $ 2gx+2fy+g^{2}+f^{2}+c=0 $
$ \therefore $ Distance $ =\frac{\frac{g^{2}+f^{2}+c}{2}-c}{\sqrt{g^{2}+f^{2}}} $
$ =\frac{g^{2}+f^{2}-c}{2\sqrt{g^{2}+f^{2}}} $ .
BETA
