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If the roots of the equation ` ( x _ 1 ^ 2 - a ^ 2 ) m ^ 2 - 2x _ 1 y _ 1 m + ( y _ 1 ^ 2 + b ^ 2 ) = 0 , ( a gt b ) ` are the slopes of two perpendicular lines intersecting at ` P (x _ 1, y _ 1 ) `, then the locus of P is

A

` x ^ 2 + y^ 2 = a ^ 2 + b ^ 2 `

B

` x ^ 2 + y ^ 2 = a ^ 2 - b ^ 2 `

C

` x ^ 2 - y ^ 2 = a ^ 2 + b ^ 2 `

D

` x ^ 2 - y^ 2 = a ^ 2 - b ^ 2 `

Text Solution

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The correct Answer is:
B
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