Question

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

Answer 1

Answer:

X = 2 cos theta - 3 sin theta , y = cos theta + 2 sin theta , eliminate theta.

1

Answer

4.0/5

84

Answer :

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 =  

sinθ =  

We know that,

sin²θ + cos²θ = 1

⇒ 5x² + 13y² + 8xy = 49,

which is the required equation.

Step-by-step explanation:

Answer 2

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