Find the equation of the circle whose center and radius are given.
center ( 5, 6), radius = 3

Question

Find the equation of the circle whose center and radius are given.
center ( 5, 6), radius = 3

radar · Answer

(x-5)^2 + (y-6)^2 = (3)^2 or 9

anonymous · Answer

(x-h)^2+(y-k)^2=r^2,h=5.k=6 and r=3

x^2+y^2-10x-12y+42=0,is the equation

anonymous · Answer

not 42,its 52

anonymous · Answer

The question that is to be filled in, = one number

anonymous · Answer

The equation I need to fill in is (x___________=_

radar · Answer

Do the math:
(x-5)^2=x^2-10x+25
(y-6)^2=y^2-12y+36    I would combine them and get
$$x ^{2}-10x+y ^{2}-12y+61=9$$ actually I would leave it as:
$$(x ^{2}-10x+25) + (y ^{2}-12y + 36) =9$$

anonymous · Answer

So is it the first equation that you posted that would fill it in or that one?

radar · Answer

I liked the first one, but they all are correct,  I don't know what your instructor is expecting as which form is the "correct" one.  I would present the first one, and then work it out to be looking like the last one.  I don't know if you have that luxury or not, if it is an on-line course which one do you have as an option?