Plz help with few qnz from Conics (1 Viewer)

[Ru$kI]

Hey peepz. Iv hit a bit of a brick wall on a few of these conics qnz, theyr all pretty similar so ill just post up one of em.

P(acos, bsin) lies on the ellipse x^2/a^2 + y^2/b^2=1 (just general eqn 4 an ellipse). The normal at P cuts the x-axis at X, and the y-axis at Y. Show that PX/PY = b^2/a^2.

I work out particular things like gradient of normal n stuff and try using eqn of normal 4 an ellipse, and try 2 play around with the data given, but cant seem 2 string it 2gether. Any help would b appreciated.

Thanx, Cyaz

Dmitri.

 

[:: ck ::]

from the top of my head...

one possible hint - use simlar triangles instead of going for the bash

 

[George W. Bush]

This question has been posted quite recently. CM_Tutor will be after you if you don't use similar triangles.

 

[Ru$kI]

Hmmm...seems wierd to use similar triangles though u'd think they would require you to get the answer using the new formulas and techniques u've just learned in this chapter, so id have to use like eqn of a tangent, eqn of a normal, gradient, etc.. besides i cant seem 2 get it even with similar triangles:S

 

[:: ck ::]

ok if u wanna do it the hard way

all u do is get equation for hte normal

sub x = 0... y = 0

once u get the coordinates

use ur distance formula for PX then PY

divide PX by PY and it shud give u the rite answer [it will be longer / more tedious than doing it using triangles]

ill post up the quick solution later on 2nite

 

[:: ck ::]

here u go

there's some unneccessary stuff on the left hand side... like finding coordinate of X...

hope u can read my handwriting as well.. haha.. gettin late =|

 

[CM_Tutor]

As GWB has suggested, I would favour a similar triangles approach - the algebra bash is a waste of time, which is a precious commodity in an exam.

A couple of thoughts - First, the questions ask for the ratio of PX / PY, so you don't actually care where X and Y are, so long as you can find the ratio. As ryan's solution shows, you only need the y-coordinate of Y, and there is an equivalent solution requiring only the x co-ordinate of X.

Second, recognising the similar triangles shows you can apply methods from different topics - this is part of the goal of the course.

Third - conics is a classic example of an area where questions in an exam penalise you time as well as marks - the algebra bash wastes time, and in addition provides the high risk of an algebraic error. Just becuase it is true that for every 5 line solution, there is a 25 line solution waiting to be found, doesn't mean that you should try and find it.