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If 2y cosθ = x sinθ and 2x secθ – y cosecθ = 3, then what is x2 + 4y2 equal to?
- a)1
- b)2
- c)4
- d)8
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
If 2y cosθ = x sinθ and 2x secθ – y cosec&thet...
2y cosθ = x sinθ
⇒ 2y = x tanθ ---- (1)
And
2x secθ – y cosecθ = 3
From equation (1);
⇒ 2x secθ – (x/2) tanθ.cosecθ = 3
⇒ 2x secθ – (x/2) secθ = 3
⇒ (3x/2) secθ = 3
⇒ x = 2cosθ
From equation (1);
2y = 2cosθ.tanθ
⇒ y = sinθ
Putting x = 2cosθ and y = sinθ in x2 + 4y2;
⇒ x2 + 4y2 = 4cos2θ + 4sin2θ
⇒ x2 + 4y2 = 4
⇒ 2y = x tanθ ---- (1)
And
2x secθ – y cosecθ = 3
From equation (1);
⇒ 2x secθ – (x/2) tanθ.cosecθ = 3
⇒ 2x secθ – (x/2) secθ = 3
⇒ (3x/2) secθ = 3
⇒ x = 2cosθ
From equation (1);
2y = 2cosθ.tanθ
⇒ y = sinθ
Putting x = 2cosθ and y = sinθ in x2 + 4y2;
⇒ x2 + 4y2 = 4cos2θ + 4sin2θ
⇒ x2 + 4y2 = 4
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