Here is the plot of the five conic sections, all of which are circles:

1. The red circle has a center at $(6, 5)$ and a radius of 4.
2. The green circle has a center at $(-5, 4.5)$ and a radius of 1.
3. The blue circle has a center at $(5, 4.5)$ and a radius of 1.
4. The orange circle has a center at $(0, -16)$ and a radius of 1.
5. The purple circle has a center at $(0, -12)$ and a large radius of approximately 24.49.

Let me know if you'd like further details or explanations on any of the steps.

Related Questions:

1. How do you derive the equation of a circle from its general form?
2. What distinguishes ellipses from circles in conic sections?
3. How can we identify a hyperbola in conic sections?
4. How would these graphs change if the centers were shifted more drastically?
5. How can conic sections be applied in real-world problems?

Tip: Remember, the key difference between a circle and an ellipse is that a circle has equal axes (radii), while an ellipse has two different axes (semi-major and semi-minor).