Question

Eliminate theath from the following: x=4cos theta-5 sin theta, y=4 sin theta +5 cos theta​

Answer 1

Answer:

x² + y² = 41

Step-by-step explanation:

Since we are given that

x =4cos(∅) - 5sin(∅)         ......(1)

y = 4sin(∅) + 5cos(∅)        .....(2)

Taking square on both sides of the equation (1)

x² = 16cos²(∅) + 25sin²(∅) - 2(cos(∅)sin(∅)        .....(3)

Taking square on the both sides of equation (2)

y² = 16sin²(∅) + 25cos²(∅) + 2(cos(∅)sin(∅)       ......(4)

Adding equation (1) and equation (2)

x² + y² = 16cos²(∅) + 25sin²(∅) - 2(cos(∅)sin(∅) + 16sin²(∅) + 25cos²(∅) +    2(cos(∅)sin(∅)  

x² + y² = 16(cos²(∅ + sin²(∅)) + 25((cos²(∅ + sin²(∅))

x² + y² = 16(1) + 25(1)   ∵ cos²(∅ + sin²(∅) = 1

x² + y² = 16 + 25 = 41

Thus after elimination of theta we get

x² + y² = 41