question_answer

 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]

A)            \[{{x}^{2}}+{{y}^{2}}={{a}^{2}}\]                             

B)            \[{{x}^{2}}-{{y}^{2}}={{a}^{2}}\]

C)            \[x+y={{a}^{2}}\]              

D)            \[{{x}^{2}}-{{y}^{2}}=4{{a}^{2}}\]

E)            \[{{x}^{2}}+{{y}^{2}}=4{{a}^{2}}\]

Correct Answer: B

Solution :

           Since the perpendicular drawn on chord from \[O(x,y)\] bisects the chord.                    \[NM=a\] \[OM=y\]                                     \[{{(ON)}^{2}}={{(OM)}^{2}}+{{(ON)}^{2}}\]                    \[{{x}^{2}}={{y}^{2}}+{{a}^{2}}\]                    \[{{x}^{2}}-{{y}^{2}}={{a}^{2}}\]