Acircle is centered at the point (5, -4) and passes through the point (-3, 2).
the equation of this circle is (x +
)2 + (y +
)2 =
.

The equation bases the center as the coordinates to put in... so the center x would go in the (x+ _)^2 part (BUT FLIP THE SIGN-- if it's at 5, then you'd write -5), and the y-center coordinate stays the same so the first part would be like this:

(x-5)^2 + (y-4)^2 (all I did was flip the x-center and keep the y-center the same and plug it in.)
Now for the equals __ part, that part is r^2. To find the radius, you can simply compare the center to the other given point, to find the distance across (aka the radius). So... From center x=5, and to point -3, that's roughly 8, so the radius is 8. BUT WAIT! It's not just r, but r^2... So, 8^2= 64... Plugging everything back in together, your answer would be:

(x-5)^2 +(y-4)^2 = 64

(x-5)^2 +(y-4)^2 = 64 that is whaty i think it is