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If the roots of the equation (x(1)^(2)...

If the roots of the equation
`(x_(1)^(2)-a^2)m^2-2x_1y_1m+y_(1)^(2)+b^2=0(agtb)` are the slopes of two perpendicular lies intersecting at `P(x_1,y_1)`, then the locus of P is

A

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

B

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

C

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

D

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

Text Solution

Verified by Experts

The correct Answer is:
B
Equation `(x_1^(2)-a^2)m^2-2x_1y_1m+y_1^(2)+b^2=0` has roots `m_1` and `m_2`
`therefore m_1m_2=(y_(1)^(2)+b^2)/(x_(1)^(2)-a^2)=-1` (Given)
`therefore x^2+y^2=a^2-b^2`
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