The conic equation is .

(a)

The general form of conic equation is .

1. If the value  , the conic is parabola.

2. If the value , the conic is an ellipse.

3. If the value and , the conic is circle.

4. If the value , the conic is hyperbola.

Here and .

, hence the equation is ellipse.  

(b)

Change the -term in the equation to term.

The new conic equation is .

Here and .

, hence the equation is hyperbola. 

(c)

Change the -term in the equation to term.

The new conic equation is .

Here and .

and , hence the equation is circle. 

(d)

The conic equation is .

For a conic equation to be a parabola, either or terms should be removed.

Remove in the conic equation.

.

Here , hence the new conic is parabola.

(a) The equation is ellipse.

(b) The equation is hyperbola.

(c) The equation is circle.

(d) Remove in the conic equation.