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If 2y cosθ = x sinθ and 2x secθ – ycosecθ = 3, then the value of (x2 + 4y2) is
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- 1
- 2
- 3
- 4
- 1
Correct Option: D
2y cosθ = x sinθ ..(i)
2x secθ – y cosecθ = 3
| ⇒ 2 . | .secθ – y cosecθ = 3 | |
| sinθ |
⇒ 4y cosecθ - y cosecθ = 3
⇒ 3y cosecθ = 3
| ⇒ y = | = sinθ | |
| 3cosecθ |
From equation (i),
2 sinθ . cosθ = x sinθ
⇒ x = 2cosθ
∴ x2 + 4y2 = 4cos2 θ + 4sin2 θ
x2 + 4y2 = 4(cos2 θ + sin2 θ) = 4
