Question 457962
{{{(x-h)^2+(y-k)^2=r^2}}} Start with the general equation of a circle.



{{{(x--4)^2+(y--6)^2=r^2}}} Plug in {{{h=-4}}} and {{{k=-6}}} (since the center is the point (h,k) ).



{{{(x--4)^2+(y--6)^2=(3)^2}}} Plug in {{{r=3}}} (this is the radius).



{{{(x--4)^2+(y--6)^2=9}}} Square {{{3}}} to get {{{9}}} (this is the radius).



{{{(x+4)^2+(y+6)^2=9}}} Simplify.



{{{(x+4)^2+(y+6)^2-9=0}}} Subtract 9 from both sides.



{{{x^2+8x+16+y^2+12x+36-9=0}}} FOIL and expand.



{{{x^2+8x+y^2+12y+43=0}}} Combine like terms.



{{{x^2+y^2+8x+12y+43=0}}} Rearrange the terms to fit the form {{{x^2+y^2+Dx+Ey+F=0}}}.



The last equation is in standard form. Here we can see that D = 8, E = 12, and F = 43.