The parametric form of the ellipse 4(x+1)2+(y-1)2=4 is

Question

The parametric form of the ellipse 4(x+1)2+(y-1)2=4 is (A) x= cos θ-1, y=2 sin θ-1 (B) x=2 cos θ-1, y= sin θ+1 (C) x= cos θ-1, y=2 sin θ+1 (D) x= cos θ+1, y=2 sin θ+1

Tardigrade Admin · Accepted Answer

Given equation of ellipse can be rewritten as ((x+1)2/1)+((y-1)2/4)=1 ∴ Parametric equations of ellipse is X+1= cos θ and y-1 =2 sin θ ⇒ x = cos θ-1 and y=2 sin θ+1

Q. The parametric form of the ellipse $4 (x + 1)^{2} + (y - 1)^{2} = 4$ is

$x = cos θ - 1, y = 2 sin θ - 1$

$x = 2 cos θ - 1, y = sin θ + 1$

$x = cos θ - 1, y = 2 sin θ + 1$

$x = cos θ + 1, y = 2 sin θ + 1$

$x = cos θ + 1, y = 2 sin θ - 1$

Given equation of ellipse can be rewritten as
$\frac{( x + 1 ) ^{2}}{1} + \frac{( y - 1 ) ^{2}}{4} = 1$
$∴$ Parametric equations of ellipse is
$X + 1 = cos θ$
and $y - 1 = 2 sin θ$
$\Rightarrow x = cos θ - 1$
and $y = 2 sin θ + 1$

Q. The parametric form of the ellipse 4(x+1)2+(y−1)2=4 is

x=cosθ−1,y=2sinθ−1

x=2cosθ−1,y=sinθ+1

x=cosθ−1,y=2sinθ+1

x=cosθ+1,y=2sinθ+1

x=cosθ+1,y=2sinθ−1

Given equation of ellipse can be rewritten as 1(x+1)2​+4(y−1)2​=1 ∴ Parametric equations of ellipse is X+1=cosθ and y−1=2sinθ ⇒x=cosθ−1 and y=2sinθ+1