Question

Please help havent found anyone who can answer will mark brainliest

Answer 1

Look at the unit circle and apply the hint. The x- and y-coordinates of each point are cosθ and sinθ, respectively. The radius of the unit circle is, of course, 1, and the center point is (0, 0).

General form of the parametric equations for a circle:

x = r·cosθ+h

and

y = r·sinθ+k

where r is the radius and (h, k) is the center. Therefore, the parametric equations for the unit circle are

x = cosθ

and

y = sinθ

:::::

The parametric equations

x = 2cosθ

and

y = 2sinθ

define a circle of radius 2, centered at the origin.

:::::

The parametric equations

x = 4cosθ

and

y = 2sinθ

define a horizontal ellipse centered at the origin, with transverse axis of length 8 and conjugate axis of length 4.

:::::

If a = b then

x = a·cosθ

and

y = b·sinθ

define a circle centered at the origin.

If a > b, then

x = a·cosθ

and

y = b·sinθ

define a horizontal ellipse centered at the origin.

If a < b, If a = b then

x = a·cosθ

and y = b·sinθ

define a vertical ellipse centered at the origin.