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Question: A circle is drawn to cut a chord of length 2a units along X-axis and to touch the Y-axis. The locus ...

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.

A

x2+y2=a2x ^ { 2 } + y ^ { 2 } = a ^ { 2 }

B

x2−y2=a2x ^ { 2 } - y ^ { 2 } = a ^ { 2 }

C

x+y=a2x + y = a ^ { 2 }

D

x2−y2=4a2x ^ { 2 } - y ^ { 2 } = 4 a ^ { 2 }

(5) x2+y2=4a2x ^ { 2 } + y ^ { 2 } = 4 a ^ { 2 }

Answer

x2−y2=a2x ^ { 2 } - y ^ { 2 } = a ^ { 2 }

Explanation

Solution

Since the perpendicular drawn on chord from O(x,y)O ( x , y ) bisects the chord.

NM=aN M = a OM=yO M = y

(ON)2=(OM)2+(ON)2( O N ) ^ { 2 } = ( O M ) ^ { 2 } + ( O N ) ^ { 2 }

x2=y2+a2x ^ { 2 } = y ^ { 2 } + a ^ { 2 }

x2−y2=a2x ^ { 2 } - y ^ { 2 } = a ^ { 2 }