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If x cos θ – y sin θ = √x² + y² cos²θ + sin²θ = 1 , then the correct relation is a² b² x² + y²
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x² - y² = 1 b² a² -
x² + y² = 1 a² b² -
x² + y² = 1 b² a² -
x² - y² = 1 a² b²
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Correct Option: B
According to question,
x cosθ – y sinθ = √x² + y²...(i)
| + | = | ...(ii) | ||||
| a² | b² | x² + y² |
| sinθ = | ||
| √x² + y² |
| cosθ = | ||
| √x² + y² |
From equation (i)
| cosθ - | sinθ = 1 | |||
| √x² + y² | √x² + y² |
| ∴ | + | = | |||
| a² | b² | x² + y² |
| ⇒ | + | = | |||
| (x² + y²)a² | (x² + y²)b² | x² + y² |
| ⇒ | + | = 1 | ||
| a² | b² |
