Solve and plot the following Conic Sections. Show your solution

 (x - 6)^2 + (y - 5)^2 = 16
 (x + 5)^2 + (y - 4.5)^2 = 1
 (x - 5)^2 + (y - 4.5)^2 = 1
100x^2 + 100(y+16)^2 = 100
x^2 + (y + 12)^2 = 600

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).

Solve and plot the following Conic Sections. Show your solution

(x - 6)^2 + (y - 5)^2 = 16
(x + 5)^2 + (y - 4.5)^2 = 1
(x - 5)^2 + (y - 4.5)^2 = 1
100x^2 + 100(y+16)^2 = 100
x^2 + (y + 12)^2 = 600

Learn how to solve and plot different circle equations from conic sections. The problem includes five circles with various centers and radii. Explore the use of the circle formula, distance formula, and other geometric concepts. Suitable for high school students in Grades 10-12.

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