Conics HSC question! (1 Viewer)

[Aysce]

Sorry it's in a link, not sure how to post it up without one D:

The problem I am having with is Q.ii. I used the definition of the ellipse where the distance from the point P to a fixed point over the distance from point P to a fixed line has the ratio of e. Again I am probably wrong, since this is a 2 marker.

 

[nightweaver066]

For those who don't want to turn their heads.

 

[Aysce]

For those who don't want to turn their heads.

Thanksss, my bad...

 

[deswa1]

I think you'll find that if T is on the directrix and the x axis, due to symmetry of the ellipse, the points P and Q both lie on the line x=ae (This is from memory so I might be wrong). Have a go using that fact

 

[Aysce]

I think you'll find that if T is on the directrix and the x axis, due to symmetry of the ellipse, the points P and Q both lie on the line x=ae (This is from memory so I might be wrong). Have a go using that fact

Yes I'm pretty sure T is the directrix too but then it would support the definition, hence the ratio would be e wouldn't it?

 

[lolcakes52]

Definition of an ellipse is a point thats distance from a line and a point are in a fixed ratio, e. So by definition PS/ST= e

 

[deswa1]

Definition of an ellipse is a point thats distance from a line and a point are in a fixed ratio, e. So by definition PS/ST= e

Yep. That's how you do it. First you have to establish that the point P is directly above the focus and then you can just use the focus directrix definition.

 

[Aysce]

So that's 2 marks right there? But then I tried to do part iii and I couldn't come up with many things + I failed miserably haha