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Question

# STATEMENT-1: The locus of the centre of a circle which touches two given circles with different radius and centre will be a hyperbola. and STATEMENT-2: If the differnece of distance of a variable point to two given is always constant and less than the distnace between the points then the locus will be a hyperbola

A
Statement -1 is True, Statement-2 is True; Statement-2 is NOT a correct expalanation for Statement-1
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B
Statement-1 is True, Statement-2 is False
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C
Statement -1 is True, Statement-2 is True; Statement-2 is a correct expalanation for Statement-1
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D
Statement-1 is False, Statement-2 is True.
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Solution

## The correct option is C Statement -1 is True, Statement-2 is True; Statement-2 is a correct expalanation for Statement-1Let r1,r2 be the radii of the given circles and r be the radius of variable circle, Let C−1,C−2,C be the centre of the given and the variable circles respectively, then CC1=r+r1 CC2=r+r2 ⇒ CC1−CC2=r1−r2

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