Math, asked by nagendra9387, 1 year ago

the equation of set of lines which are at a constant distance 2 units from the origin is

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Answered by abhi178
8

the equation of set of lines which are at a constant distance 2 units from the origin is

  1. x + y + 2 = 0
  2. x + y + 4 = 0
  3. x cosα + y sinα = 2
  4. 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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