Task 2
Choose three of the four conic sections that you learned about in this unit: parabolas, circles, ellipses, and hyperbolas. Make a detailed graph of each one that you intend on incorporating into your design to make your robot assist with household chores. For each of these graphs, be sure to label important points such as vertices, foci, axes, and directrixes. Also, identify each graph with its equation. Make sure that the equation is the same one that will be used in your final design.
1. Parabola:
Equation: y = x^2
Important Points:
- Vertex: (0, 0)
- Axis: x-axis
- Directrix: y = -1/4
(Graph not drawn due to limitations)
2. Circle:
Equation: (x-2)^2 + (y-2)^2 = 4
Important Points:
- Center: (2, 2)
- Radius: 2 units
3. Ellipse:
Equation: (x+3)^2/9 + (y-4)^2/4 = 1
Important Points:
- Center: (-3, 4)
- Major axis: 6 units (2a = 6, a = 3)
- Minor axis: 4 units (2b = 4, b = 2)
- Foci: (-3, 4±√5)
- Vertices: (-6, 4) and (0, 4)