Question

eliminate thitha if x= 2cos thitha - 3sin thitha and y= cos thitha + 2sin thitha​

Answer 1

Answer :

5x² + 13y² + 8xy = 49

Step-by-step Explanation:

Given that,

x = 2 cosθ - 3 sinθ               ----------------  (i)  and

y = cosθ + 2 sinθ

⇒ 2y = 2 cosθ + 4 sinθ       ----------------  (ii)

Now, (ii) - (i) ⇒

2y - x = 2 cosθ + 4 sinθ - 2 cosθ + 3 sinθ

⇒ 2y - x = 7 sinθ                 ----------------  (iii)

Again, (ii) × 7 ⇒

7y = 7 cosθ + 2 (7 sinθ)

⇒ 7y = 7 cosθ + 2 (2y - x)                  , by (iii)

⇒ 7 cosθ = 3y + 2x             ----------------  (iv)

Finally, we have

cosθ =  $\frac{3y+2x}{7}$

sinθ =   $\frac{2y-x}{7}$

We know that,

sin²θ + cos²θ = 1

⇒ $(\frac{2y-x}{7})^{2} + (\frac{3y+2x}{7})^2$  = 1

⇒ $(\frac{4y^2-4xy+x^2}{49})+ (\frac{9y^2+12xy+4x^2} {49})$  = 1

⇒ $(\frac{4y^2-4xy+x^2+9y^2+12xy+4x^2}{49})$  = 1

⇒ 5x² + 13y² + 8xy = 49

equation arrived without θ

Answer 2

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