Question 1037767
The general point for the parabola is  (x,y) and the directrix is {{{y=x/4-3/4}}}.


Distance from general point to either focus or directrix is equal. (Definition of a parabola).


{{{sqrt((x-2)^2+(y-3)^2)=sqrt((x-x)^2+(y-(x/4-3/4))^2)}}}-----Using the Distance Formula.


{{{(x-2)^2+(y-3)^2=0^2+(y-(x/4-3/4))^2}}}


{{{(x-2)^2+(y-3)^2=(y-x/4+3/4)^2}}}


{{{(x-2)^2+(y-3)^2=y^2-xy/4+3y/4-xy/4+x^2/16-3x/16+3y/4-3x/16+9/16}}}


{{{(x-2)^2+(y-3)^2=y^2-xy/2+x^2/16-6x/16+6y/4+9/16}}}


{{{(x-2)^2+(y-3)^2=y^2-xy/2+x^2/16-3x/8+3y/2+9/16}}}


Multiply the members by 16 to clear away denominators.
{{{16(x-2)^2+16(y-3)^2=16y^2-8xy+x^2-6x+24y+9}}}


{{{16(x^2-4x+4)+16(y^2-6y+9)=16y^2-8xy+x^2-6x+24y+9}}}


{{{16x^2-64x+64+16y^2-96y+144=16y^2-8xy+x^2-6x+24y+9}}}


{{{15x^2-64x+64-96y+144=-8xy-6x+24y+9}}}


{{{15x^2-64x+6x+64-96y-24y+8xy-9=0}}}


{{{highlight(15x^2-58x-120y+8xy+55=0)}}}