How do you find the equation in standard form of the parabola with directrix x=5 and focus (11, -7)?

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Answer 1 · 2018-07-21T14:41:58

The equation is #=x=1/12(y+7)^2+8#

Any point #(x,y)# on the parabola is equidistant from the directrix and from the focus

#(x-5)=sqrt((x-11)^2+(y+7)^2)#

Squaring both sides

#(x-5)^2=(x-11)^2+(y+7)^2#

#x^2-10x+25=x^2-22x+121+(y+7)^2#

#12x=(y+7)^2+96#

#x=1/12(y+7)^2+8#

graph{(x-1/12(y+7)^2-8)=0 [-14.88, 50.06, -18.7, 13.76]}