conics question (1 Viewer)

[aDimitri]

can someone give me a hand with the question attached? it's question 4 from the 2004 HSC. Got no clue how to go about part 2.

 

[rumbleroar]

done this and cried as i couldn;t get it but
ii - find coordinates of P by subbing T (a/e,0) into the tangent equation and just use distance formula
iii - use trig ratios (tan)
iv - area formula

 

[HeroicPandas]

For (ii), draw a diagram and see if you can use the definition of ellipses (ratio of something on something = e)

done this and cried as i couldn;t get it but
ii - find coordinates of P by subbing T (a/e,0) into the tangent equation and just use distance formula
iii - use trig ratios (tan)
iv - area formula

Hey, they chose T such that it lies on the x-axis so must P and Q be vertical?

If so, you can find point P easily by subbing in x = ae (the focus)

In the end, distance formula was not used

 

[aDimitri]

ah holy crap didn't think about P and Q being vertical! wow, that simplifies things. I was going to find P by subbing in T=a/e but it was so horrid i figured i must be missing the easier way. thanks!

 

[dinomyte]

Yeah, we did this in class and lots of people got tripped up too. My teacher recommended to redraw the diagram, because you can see it very easily after that.