The equation is .

a.

.

If , then either or .

So, either the term is zero or the term is zero.

If , then .

If , then .

Since the equations will have only one squared term, it will be the equation of a parabola. Thus, if , then the graph is a parabola. 

b.

.

Consider .

 If , then either and are both greater than , or and are both less than .

Then,  .

In both cases, the equation will have squared terms that are added.

So, it will be the equation of an ellipse.

Thus if if , the graph is an ellipse.

c.

.

if , then the equation will have squared terms that are added and it can be written so that the coefficient of both terms is 1.

Then,  or  .

So, it will be the equation of a circle.

Thus, if , then the graph is a circle.

d.

.

If , then either or .

In both cases, the equation will have squared terms that are subtracted.

Then,  or .

So, it will be the equation of a hyperbola.

Thus, if , then the graph is a hyperbola.

a. Parabola.

b. Ellipse.

c. Circle.

d. Hyperbola.