A variable line L is drawn through O(0,0) to meet the line `L_(1) " and " L_(2)` given by y-x-10 =0 and y-x-20=0 at Points A and B, respectively. Locu

Question

A variable line L is drawn through O(0,0) to meet the line `L_(1) " and " L_(2)` given by y-x-10 =0 and y-x-20=0 at Points A and B, respectively. Locu

A variable line L is drawn through O(0,0) to meet the line `L_(1) " and " L_(2)` given by y-x-10 =0 and y-x-20=0 at Points A and B, respectively.
Locus of P, if `OP^(2) = OA xx OB`, is
A. `(y-x)^(2) = 100`
B. `(y+x)^(2) = 50`
C. `(y-x)^(2) = 200`
D. none of these

Monjur Alahi

5 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 - C
`r^(2) = (10 xx 20)/("sin" theta - "cos"theta)^(2)`
`"or " (r "sin" theta - r" cos" theta)^(2) = 200`
Hence, the locus is `(y-x)^(2) = 200`.

5 views Answered 2023-02-05 15:29