Hard Conics Question (1 Viewer)

[superSAIyan2]

Prove that if chord PQ cuts hyperbola x^2/a^2 - y^2/b^2 = 1 at P and Q and the asymptotes at P' and Q' then PP' = QQ'

Can someone please show me how to do this. I tried both parametric and cartesian approach. And using distance formula gets way too complicated as there are like 3 or 4 terms inside a ()^2. Is there a simple way to do this?

Thanks

 

[hayabusaboston]

Prove that if chord PQ cuts hyperbola x^2/a^2 - y^2/b^2 = 1 at P and Q and the asymptotes at P' and Q' then PP' = QQ'

Can someone please show me how to do this. I tried both parametric and cartesian approach. And using distance formula gets way too complicated as there are like 3 or 4 terms inside a ()^2. Is there a simple way to do this?

Thanks

Im starting conics on friday, if noone has helped by then, I'll try to

 

[superSAIyan2]

thanks ... but wouldnt it take a few weeks for you to learn hyperbola properties (assuming you learn ellipse first)

 

[hayabusaboston]

Our class does shiz pretty quick aye haha but yea my teacher likes to do things quick, knowing her we'll whiz through conics in a very short space of time. So I will probably have the knowledge background to your question before the end of next week, thurs fri sometime.

This is assuming I can keep up with my teachers speed of teaching LOL.... I hope I can....

 

[RealiseNothing]

2005 HSC MX2 question 8, have a look at it.

 

[planino]

Study for 2U, b0tch

 

[superSAIyan2]

hey realise thanks for the suggestion. ive already completed that question lol - its in our 4unit booklet. but the question specifies that A (or P') is directly above P and Q' is directly below Q. Or should I just consider the triangles given in the question and use that to show the distances are equal?

 

[RealiseNothing]

hey realise thanks for the suggestion. ive already completed that question lol - its in our 4unit booklet. but the question specifies that A (or P') is directly above P and Q' is directly below Q. Or should I just consider the triangles given in the question and use that to show the distances are equal?

The question 8 is in 5 parts, the 4th part proves the distances are equal (it uses the first 3 parts though).

 

[superSAIyan2]

oh i didnt see that - thanks