Hi. heres the problem :
1. Find the equation of the parabola with focus (1,1) and directrix x+y=0, and simplify this equation to a form without radicals.
2.Let the vertex of the parabola x^2=4py be joined to every other point of the parabola. show that the midpoints of the resulting chords lie on another parabola. find the focus and directrix of the second parabola.
for the first one, I dont get how the to get the directrix. if its x+y=0 and the focus is (1,1), then the directrix should be 1-2(1/4A) or 1/2A. (because the focus is (x,y1-1/4A) so 1-1/4A should be y1 and 1-1/4A-1/4A should be the directrix. (I think). im confused as to where to go though. Any tips on this one?
the second one : im confused about the letter P. Maybe 4p = A, and the equation if I move it around is :
if this is true then the vertex is (0,0). But Im kind of confused. I cant find exact points because I have this variable p and I dont get it. but I kind of think that like... this equation : 1/4p(x/2)^2=y/2 might be the equation of the second parabola. not sure about that though. Cant find the focus and directrix of first parabola because I dont get p. Please help.