Question

Please solve this question

Answer 1

great question brother!

Given that,

x = 2 cosθ - 3 sinθ ...(i)

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 = 3y+2x/7

sinθ = 2y-x/7

We know that,

sin²θ + cos²θ = 1

putting value of sinθ and cosθ,

5x² + 13y² + 8xy = 49,

which is the required equation.

hope this helps you out......