Hi Could someone please give me hints for these last few questions I have to do....
I'm really struggling to finish them off before the weekend's over
Please, any help?
i hope you know for an ellipse .
where 2c=focal distance, 2b=minor axis length, 2a=major axis length.
So having origin as centre for the ellipse, the point (c,y) lies on the ellipse for some y which we will find.
therefore, placing (c,y) in standard ellipse eqn:
using , we get .
thus distance of point from (c,0) i.e. a focus, is which is the semi-latus rectum.
in case u dont know .
from defn. of ellipse sum of distances of a point from two focii of an ellipse is equal to length of major axis. So, for a standard ellipse having origin as centre, for the point (0,b),
dist of (0,b) from (-c,0)=dist of (0,b) from (c,0)=a. [from geometry]
the triangle formed by (0,0),(c,0),(0,b) is right angled. So from Pythagoras, .
For a general point P, the ratio SG/MP will not be constant. The simplest formulas I can get are and , from which you can see that the ratio SG/MP depends on t.