# Generating all conic sections

## Geometric context:

- Consider a line
**f**and a point**C**defined on that line. Let's draw a circle**c**with centre**C**and radius**CR**. - Consider a point
**B**on**f**, and point**A**on the circle. Reflect point**A**with respect to line**f**to determine point**A'**. - Finally, we draw the lines
**AB**and**A'C**; these lines intersect at**D**.

**D**when point

**A**is moved across the circle describes a conic section. Observe what happens when you move the point

**B**.

## Questions:

- What happens if
**B**is within the segment**EE'**? - What happens if
**B**is not in the segment**EE'**? - What happens if
**B**is equal to**E**or**E'**? - What happens if
**B**is moved far away to infinity along**f**?

**EE'**is equal to 4

**CR**.

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