Question 538337
Your problem may have been
"Find an equation for the circle centered at (2,-5), that contains the point (18,25)."
I'll solve that.
According to Pythagoras, the radius (r) of that circle, squared, is
{{{r^2=(18-2)^2+(25-(-5))^2=(16)^2+(25+5)^2=16^2+30^2=256+900=1156=34^2}}}
If a point (x,y) is in that circle, its distance to the center is also r, so according to Pythagoras,
{{{(x-2)^2+(y-(-5))^2=(x-2)^2+(y+5)^2=1156=34^2}}}
An elegant form of the equation for that circle would be
{{{(x-2)^2+(y+5)^2=34^2}}}
No memorized formulas were abused in the solving of this problem.