Help With Conics Question (1 Viewer)

[Traveller0901]

Can someone please explain to me step by step how to complete q4 & 5 from Exercise 3.3 of the Cambridge 4u textbook?

Thanks

 

[Sy123]

Its asking for PX/PY

We get X and Y from finding the normal to the ellipse at P. So that's our first step, we must determine the equation of the normal at P. Once you derive so through differentiation and otherwise we find:



So we need to find the co-ordinates of X and Y in order to find PX/PY

X is the x-intercept, so lets find it, it turns out that that:



Find the y-intercept, which corresponds with point Y



So now we have the co-ordinates of the points P, X and Y.

So now we can find the value of PX/PY

It turns out that (using distance formula)





Divide these 2

 

[darkfenrir]

Its asking for PX/PY

We get X and Y from finding the normal to the ellipse at P. So that's our first step, we must determine the equation of the normal at P. Once you derive so through differentiation and otherwise we find:



So we need to find the co-ordinates of X and Y in order to find PX/PY

X is the x-intercept, so lets find it, it turns out that that:



Find the y-intercept, which corresponds with point Y



So now we have the co-ordinates of the points P, X and Y.

So now we can find the value of PX/PY

It turns out that (using distance formula)





Divide these 2

wow, this guy.....

the shelley she of 2013 man! hahahhaa

 

[Traveller0901]

@Sy123- Once again, thankyou so much for explaining it!