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)`

Question

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)`

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. `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`

Monjur Alahi

4 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Salim Ahmed Kawsar

Correct Answer - 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`

4 views Answered 2023-02-05 15:29