The equation of a circle with center (a, b) and center r, is:
[tex]\displaystyle{ (x-a)^2+(y-b)^2=r^2[/tex].
We have the center, so we can substitute a=5, and b=-4 in the equation. But we still need the radius.
The radius of a circle is the distance between the center ( (5, -4) ) and any point of the circle ( (-3, 2) ). Using the formula of the distance between 2 points, we have:
[tex]\displaystyle{ r= \sqrt{(5-(-3))^2+(-4-2)^2}= \sqrt{8^2+(-6)^2}= \sqrt{64+36}=10[/tex].
Substituting in the equation, we have:
[tex]\displaystyle{ (x-5)^2+(y-(-4))^2=10^2[/tex],
that is [tex]\displaystyle{ (x-5)^2+(y+4)^2=100[/tex].
Answer: (x +_(-5)_ )^2 + (y +_4_ )^2 = _100_
