Answer:
If you've more doubts you can ask :)
Step-by-step explanation:
If the centre of a circle is (a, b) and radius r, then the equation of the circle is :
[tex](x - x)^2 + (y-b)^2 = r^2[/tex]
First we will find the centre, (a , b):
[tex]a = \frac{3+(-1)}{2} = \frac{2}{2} = 1\\\\b = \frac{-2 + 4}{2} = \frac{2}{2} = 1[/tex]
Find radius:
[tex]Radius, r = \frac{Diameter}{2}[/tex]
Diameter is the distance between (-1, 4) and (3, -2)
[tex]diameter = \sqrt{(x_2 - x_1)^2 +(y_2-y_1)^2} \\\\[/tex]
[tex]= \sqrt{(3-(-1)^2 + (-2-4)^2} \\\\=\sqrt{16 + 36}\\\\=\sqrt{52}\\\\=\sqrt{4 \times 13}\\\\=2\sqrt{13} \ units[/tex]
Therefore , [tex]r = \frac{2 \times \sqrt{13} }{2} = \sqrt{13} \ units[/tex]
Equation of the circle is :
[tex](x - 1)^2 +(y-1)^2 = 13[/tex]
