hi i was wondering how would you find the equation of a parabola with it's vertex at -2,0, and with no directrix or focus given. the parobala opens toward the left. the two choices in my multiple choice answer sheet that sound the most logical would be x+2=-1/8y^2 and x-2=1/8y^2.

Question

hi i was wondering how would you find the equation of a parabola with it's vertex at -2,0, and  with no directrix or focus given. the parobala opens toward the left. the two choices in my multiple choice answer sheet that sound the most logical would be x+2=-1/8y^2 and x-2=1/8y^2.

drwls · Answer

x + 2 = -1/8y^2 would be the choice, because its highest x value is -2, at y=0. The coeffient in from of the y^2 could be any positive number - it deterrmines where the focus and directrix are.