it's late and i cant get these 2 question to fall out! help please
I have point on ellipse
I have the tangent and normal to this ellipse meet Y-axis at T and N. Then i found the centre of the circle through T,N,P to be
The last part asks for the equation of the locus of Q on PX produced such that X is the midpoint of PQ
so ive let Q=(x,y) then
but i cant find the locus. The book says
i cant get this with my Q. Maybe im making a mistake or my Q is wrong or the book is wrong......
Also having trouble with this:
the tangent at to
cuts the Y-axis at Q. The normal at P is parallell to the line joining Q to one focus S'. If S is the other focus, show that PS is parallel to the y-axis.
found Q to be
but QS parallel to normal so grad normal= grad QS
now im assuming i use the grad QS=grad normal to show the denominator of grad PS=0 but i cant seem to get it....