Question 784559
The distance from a point {{{P(x[P],y[P])}}} to a line with the equation {{{ax+by+c=0}}} can be calculated ad
{{{abs(ax[P]+by[P]+c)/sqrt(a^2+b^2)}}}
 
If the line with equation {{{12x+5y-26=0}}} is tangent to the circle, the distance from the line to the center of the circle is the radius of the circle.
{{{a=12}}}, {{{b=5}}}, {{{c=26}}}, {{{P(2,3)}}} has {{{x[P]=2}}}, {{{y[P]=3)}}}
That distance is
{{{abs(12*2+5*3-26)/sqrt(12^2+5^2)=abs(24+15-26)/sqrt(144+25)=13/sqrt(169)=13/13=highlight(1)}}}
h{{{highlight(1)}}} distance is the radius of the circle, so the equation of the circle in center-radius form is
{{{(x-2)^2+(y-3)^2=1^2}}} --> {{{highlight((x-2)^2+(y-3)^2=1)}}}
That is what I have seen called "standard form".
The other popular form is
{{{(x-2)^2+(y-3)^2=1}}} --> {{{x^2-4x+4+y^2-6y+36=1}}} --> {{{x^2-4x+y^2-6y+40=1}}} --> {{{highlight(x^2-4x+y^2-6y+39=0)}}}, and I've seen that called "general form".