Question

eliminate theta from the following:

2x = 3 - 4tan theta, 3y = 5 + 3sec theta

Answer 1

Step-by-step explanation:

3y = 5 + 3secθ

3secθ = 5-3y

secθ = (5-3y)/3

(secθ)² = (5-3y)²/9

Now,

2x = 3 - 4tanθ

4tanθ = 3-2x

tanθ = (3-2x)/4

(tanθ)² = (3-2x)²/16

1 + (tanθ)² =1 + (3-2x)²/16

(5-3y)²/9 = (16 + 9 + 4x² -12x)/16

(25 + 9y² -30y)16 = 9(25 + 4x² -12x)

400 + 144y² - 480y = 225 + 36x² - 108x

175 + 144y² - 480y = 36x² - 108x

144y² - 480y-36x² + 108x +175 = 0