Alternative methods to this conics question (1 Viewer)

[Dimsimmer]

This is from the Cambridge textbook in the diagnostic test.

P(a coso, bsino) lies on the ellipse x^2/a^2+y^2/b^2=1. The tangent at P cuts the x-axis at X and the y-axis at Y. Show that PX/PY=b^2/a^2. I know that this could be done with the distance formula, but since i find it time consuming, are there any better alternative methods to this question?

o stands for theta

Thanks.

 

[_ShiFTy_]

I dont think theres another way...tho u could do dividing intervals or something, but thats a retarded method and might get u marked down

 

[Trev]

Using similar triangles will work.
Draw a line perpendicular to the y-axis from point P and a line perpendicular to the x-axis from point P, this will make your two triangles.

 

[Mountain.Dew]

I dont think theres another way...tho u could do dividing intervals or something, but thats a retarded method and might get u marked down

i dont think u would get marked down, as long as its shown correct and sound mathematical logical progression.

 

[lovelyq00]

what do u mean dividing intervals?

 

[Mountain.Dew]

what do u mean dividing intervals?

i think what _ShiFTy_ means by dividing intervals IS that the 'intervals' are divided into a certain ratio, usually called m:n. this ratio is determined by a pt that lies on the interval.

so, say in the interval AB (A and B are two distinct pts), when P divides AB in the ratio 4:3, that means that AP = 4 WHERE BP = 3. So, if AP just so happened to be 24 units, then BP would be 3/4 of 24, or 18 units. still abides by the ratio 4:3.