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  1. If x cos θ – y sin θ = √x² + y²
    cos²θ
    +
    sin²θ
    =
    1
    , then the correct relation is
    a²b²x² + y²
    1. x²
      -
      y²
      = 1
      b²a²
    2. x²
      +
      y²
      = 1
      a²b²
    3. x²
      +
      y²
      = 1
      b²a²
    4. x²
      -
      y²
      = 1
      a²b²
Correct Option: B

According to question,
x cosθ – y sinθ = √x² + y²...(i)

cos²θ
+
sin²θ
=
1
...(ii)
a²b²x² + y²


sinθ =
- y
√x² + y²

cosθ =
x
√x² + y²

From equation (i)
x
cosθ -
y
sinθ = 1
√x² + y²√x² + y²

∴
cos²θ
+
sin²θ
=
1
a²b²x² + y²

⇒
x²
+
y²
=
1
(x² + y²)a²(x² + y²)b²x² + y²

⇒
x²
+
y²
= 1
a²b²



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