$\"\"$

\

The parametric equation is $\"\"$ and $\"\"$ .

\

(a)

\

Consider $\"\"$ .

\

$\"\"$ .

\

Consider $\"\"$ .

\

$\"\"$ .

\

Trigonometric identity : $\"\"$ .

\

$\"\"$

\

The curve equation $\"\"$ represents a circle equation with center at origin and radius of $\"\"$ units.

\

$\"\"$

\

(b)

\

The parametric equation is $\"\"$ and $\"\"$ .

\

Consider $\"\"$ .

\

$\"\"$

\

$\"\"$ .

\

Consider $\"\"$ .

\

$\"\"$

\

$\"\"$ .

\

Trigonometric identity : $\"\"$ .

\

$\"\"$

\

The curve equation $\"\"$ represents a circle equation with center at $\"\"$ and radius of $\"\"$ units.

\

The center of the circle shifted from origin to $\"\"$ .

\

$\"\"$

\

(c)

\

The sine and cosine are interchanged.

\

The parametric equation is $\"\"$ and $\"\"$ .

\

Consider $\"\"$ .

\

$\"\"$ .

\

Consider $\"\"$ .

\

$\"\"$ .

\

Trigonometric identity : $\"\"$ .

\

$\"\"$

\

The curve equation $\"\"$ represents a circle equation with center at origin and radius of $\"\"$ units.

\

But the curve starts from $\"\"$ where the curve in (a) starts at $\"\"$ .

\

$\"\"$

\

(a) The curve equation $\"\"$ represents a circle equation with center at origin and radius of $\"\"$ units.

\

(b) The curve equation $\"\"$ represents a circle equation with center at $\"\"$ and radius of $\"\"$ units.

\

The center of the circle shifted from origin to $\"\"$ .

\

(c) The curve starts from $\"\"$ where the curve in (a) starts at $\"\"$ .