Circle And System Of Circles Question 134
Question: The locus of the centre of the circle which cuts a chord of length 2a from the positive x-axis and passes through a point on positive y-axis distant b from the origin is
Options:
A) $ x^{2}+2by=b^{2}+a^{2} $
B) $ x^{2}-2by=b^{2}+a^{2} $
C) $ x^{2}+2by=a^{2}-b^{2} $
D) $ x^{2}-2by=b^{2}-a^{2} $
Show Answer
Answer:
Correct Answer: C
Solution:
Here $ 2\sqrt{g^{2}-c}=2a\Rightarrow g^{2}-a^{2}-c=0 $ …..(i) and it passes through (0, b), therefore $ b^{2}+2fb+c=0 $ ………….(ii)
On adding (i) and (ii), we get $ g^{2}+2fb=a^{2}-b^{2} $
Hence locus is $ x^{2}+2by=a^{2}-b^{2} $ .
BETA
