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Stuck on this conic question?

A conic has eccentricity e=0.7, a focus (5,−3) and directrix y=2x−7. Find the points of intersection of the conic with line y=−3.
I'm really stuck on this, and have no idea even where to start.
Any help guys?
Reply 1
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TeeEm
19
Original post by alex2100x
A conic has eccentricity e=0.7, a focus (5,−3) and directrix y=2x−7. Find the points of intersection of the conic with line y=−3.
I'm really stuck on this, and have no idea even where to start.
Any help guys?


eccentricity less than 1 is an ellipse...do you know the definition of e in the locus of a conic?
Reply 2
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alex2100x
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Original post by TeeEm
eccentricity less than 1 is an ellipse...do you know the definition of e in the locus of a conic?


No I do not. I also don't understand the relevance of the directrix, my lecturer didn't even mention directrix in relation to ellipses only parabolas :frown: care to enlighten me?
Reply 3
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TeeEm
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Original post by alex2100x
No I do not. I also don't understand the relevance of the directrix, my lecturer didn't even mention directrix in relation to ellipses only parabolas :frown: care to enlighten me?


an ellipse is the locus of a point whose distance from a fixed point(focus) to that from a fixed line(directrix) remains constant (e).
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alex2100x
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Original post by TeeEm
an ellipse is the locus of a point whose distance from a fixed point(focus) to that from a fixed line(directrix) remains constant (e).


Never seen it defined that way only seen it defined as the sum of two distances from two foci remains constant. I will check over the question again and report back!
Reply 5
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TeeEm
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Original post by alex2100x
Never seen it defined that way only seen it defined as the sum of two distances from two foci remains constant. I will check over the question again and report back!


ALL CONIC SECTIONS are defined as a locus using focus and directrix where different values of e produce different conics

e.g.
e=0 circle
0<e<1 ellipse
e=1 parabola
e>1 hyperbola (special case e=√2 rectangular hyperbola)


... the sum of two distances from two foci remains constant...

is a consequence of the definition which can easily be proven using the general definition
Reply 6
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alex2100x
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Original post by TeeEm
ALL CONIC SECTIONS are defined as a locus using focus and directrix where different values of e produce different conics

e.g.
e=0 circle
0<e<1 ellipse
e=1 parabola
e>1 hyperbola (special case e=√2 rectangular hyperbola)


... the sum of two distances from two foci remains constant...

is a consequence of the definition which can easily be proven using the general definition


didn't even know this and now I can't do any of the questions :sigh: sorry for wasting your time :frown:
Reply 7
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TeeEm
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Original post by alex2100x
didn't even know this and now I can't do any of the questions :sigh: sorry for wasting your time :frown:


my time is not wasted ...
What course do you do and what prior knowledge do you have?
Reply 8
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alex2100x
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Original post by TeeEm
my time is not wasted ...
What course do you do and what prior knowledge do you have?


First year undergrad. A level/gcse maths.
Reply 9
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TeeEm
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Original post by alex2100x
First year undergrad. A level/gcse maths.


undergrad in what subject?
Reply 10
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alex2100x
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Original post by TeeEm
undergrad in what subject?


Maths
Reply 11
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TeeEm
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Original post by alex2100x
Maths



o.k.


look at this reference on conics first

CONIC SECTION REFERENCE.pdf
Reply 12
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TeeEm
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Original post by alex2100x
Maths


next look at the link

http://www.madasmaths.com/archive/maths_booklets/further_topics/various/conic_sections.pdf

this is FP3 level standard, but it has full solutions.


your question is way above further maths

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