(i)

The parametric equations is and .

Consider .

.

Substitute in .

.

The equation represents a horizontal parabola with vertex at .

The function is continuous for all values of .

Observe the graphs:

The above specifications matches to the graph (f).

(ii)

The parametric equations is and .

Consider .

.

Substitute in .

.

The equation represents a horizontal parabola with vertex at .

For a sine function: .

The values lie between .

For a sine function: .

The values lie between .

Observe the graphs:

The above specifications matches to the graph (c).

(iii)

The parametric equations of Lissajous curve is and .

For a cosine function: .

The values lie between .

For a sine function: .

The values lie between .

Observe the graphs:

The above specifications matches to the graph (d).

(iv)

The parametric equations of evolute of ellipse is and .

For a cosine function: .

The values lie between .

For a sine function: .

The values lie between .

Observe the graphs:

The above specifications matches to the graph (a).

(v)

The parametric equations of Involute of circle is and .

Consider (-axis)

Therefore along -axis, the point on the curve is .

Observe the graphs:

The above specifications matches to the graph (b).

(vi)

The parametric equations of Serpentine curve is and .

For a cotangent function: .

The range of is .

Observe the graphs :

The above specifications matches to the graph (e).

(i) The equation matches to the graph (f).

(ii) The equation matches to the graph (c).

(iii) The equation matches to the graph (d).

(iv) The equation matches to the graph (a).

(v) The equation matches to the graph (b).

(vi) The equation matches to the graph (e).