Circle And System Of Circles Question 106
Question: The locus of the centre of the circle which cuts off intercepts of length $ 2a $ and $ 2b $ from x-axis and y-axis respectively, is
Options:
A) $ x+y=a+b $
B) $ x^{2}+y^{2}=a^{2}+b^{2} $
C) $ x^{2}-y^{2}=a^{2}-b^{2} $
D) $ x^{2}+y^{2}=a^{2}-b^{2} $
Show Answer
Answer:
Correct Answer: C
Solution:
$ 2\sqrt{g^{2}-c}=2a $ ………….(i) $ 2\sqrt{f^{2}-c}=2b $ ………….(ii) On squaring (i) and (ii) and then subtracting (ii) from (i), we get $ g^{2}-f^{2}=a^{2}-b^{2}. $
Hence the locus is $ x^{2}-y^{2}=a^{2}-b^{2} $ .
BETA
