Question 944672
We get
x^2+y^2+6x-8y+25=16+x^2+y^2-6x-8y+25+8sqrt(x^2+y^2-6x-8y+25)
12x-16=8sqrt(x^2+y^2-6x-8y+25)
3x-4=2sqrt(x^2+y^2-6x-8y+25)
Squaring on both sides
9x^2+16-24x=4(x^2+y^2-6x-8y+25)
5x^2-4y^2+32y-84=0