Step 1
a) Consider the equation It is known that the equation of conic section is in the form In the given equation, the coefficient of , respectively, which means that is, . Therefore, this is the equation of a hyperbola. Hence, the conic section of the given equation is a hyperbola.
Step 2
b) Consider the equation It is known that the equation of conic section is in the form Here, the given equation does not have the term of , which means that is, . Therefore, this is the equation of parabola. Hence, the conic section of the given equation is a parabola. Step 3 c) Consider the equation It is known that the equation of conic section is in the form . In the given equation, the coefficient of and are and respectively, which means that is, . Therefore, this is the equation of an ellipse. Hence, the conic section of the given equation is an ellipse.