Question

把下列参数方程代为普通方程:① x=1-2cosθ y=-2-sinθ (θ为参数) ② x=2+4tanθ y=-1+3secθ (θ为参数

把下列参数方程代为普通方程:
① x=1-2cosθ
y=-2-sinθ
(θ为参数)
② x=2+4tanθ
y=-1+3secθ
(θ为参数)

Answer 1

① (x - 1)/2 = -cosθ ~ (i)
y + 2 = -sinθ ~ (ii)
(i)² + (ii)²:[(x - 1)/2]² + (y + 2)² = (-cosθ)² + (-sinθ)² (sin²θ + cos²θ = 1)
(x - 1)²/4 + (y + 2)² = 1

② (x - 2)/4 = tanθ ~ (iii)
(y + 1)/3 = secθ ~ (iv)
(iv)² - (iii)²: [(y + 1)/3]² - [(x - 2)/4]² = secθ² - tanθ² (1 + tan²θ = sec²θ)
-(x - 2)²/16 + (y + 1)²/9 = 1