Answer:
![(x-5)^2 + (y+4)^2 = 10^2](https://tex.z-dn.net/?f=%28x-5%29%5E2%20%20%2B%20%28y%2B4%29%5E2%20%3D%2010%5E2)
Step-by-step explanation:
We need to find the equation of the circle. First, the formula:
![(x-h)^2 + (y-k)^2 = r^2](https://tex.z-dn.net/?f=%28x-h%29%5E2%20%2B%20%28y-k%29%5E2%20%3D%20r%5E2)
Where (h,k) is the center and r is the radius
The center is (5,-4), so we can say:
![(x-5)^2 + (y+4)^2 = r^2](https://tex.z-dn.net/?f=%28x-5%29%5E2%20%20%2B%20%28y%2B4%29%5E2%20%3D%20r%5E2)
Now, to find the radius, we can use the distance formula to find distance between (5,4) and (-3,2).
The distance formula is ![\sqrt{(y_2-y_1)^2 + (x_2-x_1)^2}](https://tex.z-dn.net/?f=%5Csqrt%7B%28y_2-y_1%29%5E2%20%2B%20%28x_2-x_1%29%5E2%7D)
Where
x_1 = 5
x_2 = -3
y_1 = 4
y_2 = 2
Plugging in, we get:
![\sqrt{(2+4)^2 + (-3-5)^2} \\=\sqrt{6^2 + 8^2}\\ =\sqrt{100} \\=10](https://tex.z-dn.net/?f=%5Csqrt%7B%282%2B4%29%5E2%20%2B%20%28-3-5%29%5E2%7D%20%5C%5C%3D%5Csqrt%7B6%5E2%20%2B%208%5E2%7D%5C%5C%20%3D%5Csqrt%7B100%7D%20%5C%5C%3D10)
Hence, the radius is 10 and we can write the equation of circle as:
![(x-5)^2 + (y+4)^2 = 10^2](https://tex.z-dn.net/?f=%28x-5%29%5E2%20%20%2B%20%28y%2B4%29%5E2%20%3D%2010%5E2)