3 hard conics q's (1 Viewer)

[jonnathann]

1.) tangent at a point P of the ellipse x^2/a^2 + y^2/b^2 = 1 (general eqn) cuts x-axis at T and the perpendicular PN is drawn to x-axis. Prove ON.OT=a^2 (i got ON.OT=a^2-b^2 :S)

2.) find the eqn of the ellipse with centre origin and foci at points (-5root3,0) and (5root3,0) given it passes through the point (8,3)

3.) P is the point (acos theta , bsiin theta) on the ellipse x^2/a^2 + y^2/b^2 = 1. Show that SP =a(1-ecos theta) and prove that PS, PS' is independent of the position of P on the ellipse.

Thanks in advance

 

[Euler]

I don't know how long it's been, but no-one's jumped onto them yet...so here goes:

1. ON.OT = a^2 is what you want. Results falls out once coordinates of N and T are found. Try using P(acos theta, bsin theta) and then working out N and T.

2. if ellipse is x^2/a^2 + y^2/b^2 = 1, then b^2=a^2(1-e^2) and foci are (ae,0) and (-ae,0). I think you can then work out what a^2 is and you are almost done. (I didn't do it.)

3. I haven't written it down, but try using the locus definition of the ellipse. The second part, you probably want to prove that PS + PS' is independent of P (in fact, PS+PS' = 2a)

hope that helps.

 

[SeDaTeD]

Oh boy, I probably would be capable of doing them but it's been so long after school. My brained has turned to mush.

 

[jonnathann]

ohh yeahh hahaha k thnx

 

[Slidey]

I don't know how long it's been, but no-one's jumped onto them yet...

Most people aren't up to conics, yet.

 

[jonnathann]

hmm we've nearli finished it
jus a few more proofs for hyperbola

 

[wanton-wonton]

Most people aren't up to conics, yet.

My school hasn't even started 4U yet. Nothing to worry, plenty of time.

 

[jumb]

My school hasn't even started 4U yet. Nothing to worry, plenty of time.

3 terms? That isnt plenty of time.

Anyway, we didnt start conics till term 1.

 

[Slidey]

^ He goes to one of the the more elite selective schools, so his teacher probably figures they can do it.

 

[Euler]

Most people aren't up to conics, yet.

I suppose that explains it! thanks...