Question 167782
Let take {{{w =(x^2+y^2-6y+9)}}}
Let take {{{z =(x^2+y^2+6y+9)}}}
Note that w-z = -12y
then 

{{{sqrt(w)-sqrt(z)=2}}}
then
{{{(sqrt(w)-sqrt(z))^2=2^2}}}
{{{w+z-2sqrt(w)sqrt(z)=4}}}
then
{{{w+z-4=2sqrt(w)sqrt(z)}}}
then
{{{(w+z-4)^2=(2sqrt(w)sqrt(z))^2}}}
then
{{{w^2+z^2+16+2wz-8w-8z=4wz}}}

{{{w^2+z^2+16-2wz-8w-8z=0}}}

{{{(w-z+4)(-z+w+4)-16w=0}}}

then

{{{(-12y+4)(12y+4)=16(x^2+y^2-6y+9)}}}


{{{144y^2+16=16(x^2+y^2-6y+9)}}}


{{{16x^2-128y^2-96y+128=0}}}