What is the standard form of the equation of the parabola with a directrix at x=-9 and a focus at (-6,7)?

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Answer 1 · 2018-06-16T17:57:06

The equation is
#(y-7)^2=6(x+15/2)#

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

#(x+9)=sqrt((x+6)^2+(y-7)^2)#

#(x+9)^2=(x+6)^2+(y-7)^2#

#x^2+18x+81=x^2+12x+36+(y-7)^2#

#6x+45=(y-7)^2#

The standard form is

#(y-7)^2=6(x+15/2)#

graph{((y-7)^2-6(x+(15/2)))=0 [-18.85, 13.18, -3.98, 12.04]}