Answer:
[tex](x-5)^2 + (y+4)^2 = 10^2[/tex]
Step-by-step explanation:
We need to find the equation of the circle. First, the formula:
[tex](x-h)^2 + (y-k)^2 = r^2[/tex]
Where (h,k) is the center and r is the radius
The center is (5,-4), so we can say:
[tex](x-5)^2 + (y+4)^2 = r^2[/tex]
Now, to find the radius, we can use the distance formula to find distance between (5,4) and (-3,2).
The distance formula is [tex]\sqrt{(y_2-y_1)^2 + (x_2-x_1)^2}[/tex]
Where
x_1 = 5
x_2 = -3
y_1 = 4
y_2 = 2
Plugging in, we get:
[tex]\sqrt{(2+4)^2 + (-3-5)^2} \\=\sqrt{6^2 + 8^2}\\ =\sqrt{100} \\=10[/tex]
Hence, the radius is 10 and we can write the equation of circle as:
[tex](x-5)^2 + (y+4)^2 = 10^2[/tex]
