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The eliminant of q from x cosθ – y sin θ = 2 and x sin θ + y cos θ = 4 will give
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- x² + y² = 20
- 3x² + y² = 20
- x² - y² = 20
- 3x² - y² = 10
Correct Option: A
x cos θ – y sin θ = 2
x sin θ + y cos θ = 4
On squaring both the equations and adding
x²cos²θ + y²sin²θ – 2 xy sin θ . cos θ + x²sin²θ + y² cos²θ + 2xy sin θ . cos θ
= 4 + 16
⇒ x² (cos²θ + sin²θ ) + y²
(sin²θ + cos²θ ) = 20
⇒ x² + y² = 20
