What is the standard form of the equation of the parabola with a directrix at x=110 and a focus at (18,41)?

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Answer 1 · 2016-05-30T13:03:57

#y^2+184x-82y-10095=0#

Let their be a point #(x,y)# on parabola. Its distance from focus at #(18,41)# is

#sqrt((x-18)^2+(y-41)^2)#

and its distance from directrix #x=110# will be #|x-110|#

Hence equation would be

#sqrt((x-18)^2+(y-41)^2)=(x-110)# or

#(x-18)^2+(y-41)^2=(x-110)^2# or

#x^2-36x+324+y^2-82y+1681=x^2-220x+12100# or

#y^2+184x-82y-10095=0#

graph{y^2+184x-82y-10095=0 [-746.7, 533.3, -273.7, 366.3]}