HELP conics question (1 Viewer)

[EliteMasterPro]

cambridge 4U
EX 3.3
Q5.

P(asec theta,btain theta) lies on the hyperbola [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=sin^2 theta and deduce that if p is an extremity of a latus rectum, then PX/PY = [e^2-1]/[e^2]

plz help... tried doing it.. wrote about 6 pages of working out but going no where... thx

 

[Giant Lobster]

btain theta? lmao its even spelt fobbish
ok this is one of those questions which test your skills in choosing the easiest method

u can use either external bisector method, or similar triangles.
with similar triangles its slightly easier imo
construct right triangles PXA and PYB, with right angles at A and B. the prove PA / PB = sin^2@ and ur done. PA and PB are just y values. Total: about half a page of working out.

Stop using distance formula.

 

[EliteMasterPro]

thank you very much for your help

appreciate it