The equation is where .

(a)

If .

Consider the equation .

.

The vertex of the parabola is and the axis of symmetry is parallel to -axis.

(b)

Find the vertical line when .

Substitute in .

.

Substitute .

If then is a single vertical line.

(C)

Find the number of  vertical line when .

Substitute in .

.

Substitute .

and .

If then the parabola has two vertical lines.

(D)

Find the number of  vertical line when .

Substitute in .

.

If then there is no real solution.

(a) The vertex of the parabola is and the axis of symmetry is parallel to -axis.

(b) If then is a single vertical line.

(c) If then the parabola has two vertical lines.

(d) If then there is no real solution.