Question 81488
a parabola is made up of points that are equidistant from a given point (focus) and a given line (directrix)


the "distance formula" gives the distance between (x,y) and (3,8) as {{{sqrt((x-3)^2+(y-8)^2)}}}


the distance between (x,y) and y=4 is y-4 ... x is not involved


setting these equal gives {{{sqrt((x-3)^2+(y-8)^2)=y-4}}} ... squaring both sides gives {{{(x-3)^2+(y-8)^2=(y-4)^2}}}


{{{x^2-6x+9+y^2-16y+64=y^2-8y+16}}} ... {{{x^2-9x+64+9-16=y^2-8y-y^2+16y}}} ... {{{x^2-9x+57=8y}}}


so {{{y=x^2/8-9x/8+57/8}}}  ........THIS ANSWER HAS BEEN CORRECTED (with my apologies)