the equation of set of lines which are at a constant distance 2 units from the origin is
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the equation of set of lines which are at a constant distance 2 units from the origin is
- x + y + 2 = 0
- x + y + 4 = 0
- x cosα + y sinα = 2
- x cosα + y sinα = 1/2
solution : let equation of line is, ax + by + c = 0
a/c to question,
distance of lines from the origin = 2 units
⇒|a(0) + b(0) + c|/√(a² + b²) = 2
⇒|c|/√(a² + b²) = 2
⇒c/√(a² + b²) = ±2 ........(1)
here equation of line is ax + by + c = 0
⇒[a/√(a² + b²)]x + [b/√(a² + b²)]y + c/√(a² + b²) = 0
⇒[a/√(a² + b²)]x + [b/√(a² + b²)]y ± 2 = 0 [from eq (1).]
let a/√(a² + b²) = cosα then b/√(a² + b²) = sinα
so equation is x cosα + y sinα ± 2 = 0
i.e., x cosα + y sinα = 2 or x cosα + y sinα = -2
Therefore option (3) x cosα + y sinα =2, is correct choice.
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