Circle And System Of Circles Question 230
Question: A circle is drawn to cut a chord of length 2a units along X-axis and to touch the Y-axis. The locus of the centre of the circle is
[Kerala (Engg.) 2005]
Options:
A) $ x^{2}+y^{2}=a^{2} $
B) $ x^{2}-y^{2}=a^{2} $
C) $ x+y=a^{2} $
D) $ x^{2}-y^{2}=4a^{2} $
E) $ x^{2}+y^{2}=4a^{2} $
Show Answer
Answer:
Correct Answer: B
Solution:
Since the perpendicular drawn on chord from $ O(x,y) $ bisects the chord. $ NM=a $
$ OM=y $
$ {{(ON)}^{2}}={{(OM)}^{2}}+{{(ON)}^{2}} $
$ x^{2}=y^{2}+a^{2} $
$ x^{2}-y^{2}=a^{2} $
BETA
