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FP3: directrix

the distance PS/ the distance PM (PS/PM) = e

what is e? I dont understand: is it the the distance between S & M?
(edited 6 years ago)
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Original post by Maths&physics
the distance PS/ the distance PM (PS/PM) = e

what is e? I dont understand: is it the the distance between S & M?


ee is a constant called the eccentricity. It is the ratio of PSPM\frac{PS}{PM} as shown in your diagram.
Original post by ManLike007
ee is a constant called the eccentricity. It is the ratio of PSPM\frac{PS}{PM} as shown in your diagram.


PS is the distance between points P & S?
Original post by Maths&physics
PS is the distance between points P & S?


Yes

PSPS is the distance between PP and SS

PMPM is the distance between PP and MM
Original post by ManLike007
Yes

PSPS is the distance between PP and SS

PMPM is the distance between PP and MM


what is a distance divided by a distance?
Original post by Maths&physics
what is a distance divided by a distance?


Distance divided by distance would give you no units so it's a ratio
Original post by ManLike007
Distance divided by distance would give you no units so it's a ratio


because the units would cancel?

superb.

the ratio will always be the same for the same ellipse but different if the ellipse is a different size? :smile:
Original post by Maths&physics
because the units would cancel?


Yh so the base unit for distance is meters so mm=1\frac{m}{m}=1, hence it's dimensionless.

Original post by Maths&physics
superb.


Indeed

Original post by Maths&physics

the ratio will always be the same for the same ellipse but different if the ellipse is a different size? :smile:


I assume so yes (though you may want to check) so using your diagram, it's worth noting that

If 0<e<10<e<1, the point P describes an ellipse.

If e=1e=1, the point P describes a parabola.

If e>1e>1 the point P describes a hyperbola.

I don't know this off the top of my head so credit to the FP3 text book.
Original post by ManLike007
Yh so the base unit for distance is meters so mm=1\frac{m}{m}=1, hence it's dimensionless.



Indeed



I assume so yes (though you may want to check) so using your diagram, it's worth noting that

If 0<e<10<e<1, the point P describes an ellipse.

If e=1e=1, the point P describes a parabola.

If e>1e>1 the point P describes a hyperbola.

I don't know this off the top of my head so credit to the FP3 text book.


thanks
Original post by ManLike007
Yh so the base unit for distance is meters so mm=1\frac{m}{m}=1, hence it's dimensionless.

Indeed



I assume so yes (though you may want to check) so using your diagram, it's worth noting that

If 0<e<10<e<1, the point P describes an ellipse.

If e=1e=1, the point P describes a parabola.

If e>1e>1 the point P describes a hyperbola.

I don't know this off the top of my head so credit to the FP3 text book.


How would e (the ratio) look like in relation to the graph? Thanks
bump
Original post by ManLike007
Yh so the base unit for distance is meters so mm=1\frac{m}{m}=1, hence it's dimensionless.



Indeed



I assume so yes (though you may want to check) so using your diagram, it's worth noting that

If 0<e<10<e<1, the point P describes an ellipse.

If e=1e=1, the point P describes a parabola.

If e>1e>1 the point P describes a hyperbola.

I don't know this off the top of my head so credit to the FP3 text book.


and is the x coordinate of the directrix a/e?
I was overthinking it. ive just watched a tutorial which explains it clearly. thanks

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