Question

Write the equation of a circle with center at (3, -2), which also passes through the point (0, 2).

Answer 1

$\text{The equation of acircle:}\\\\(x-h)^2+(y-k)^2=r^2\\\\(h;\ k)-center\\r-radius\\\\\text{We have center}\ (3,\ -2)\to h=3\ \text{and}\ k=-2.\\\\\text{The radius is the distance between the points} (3,\ -2)\ \text{and}\ (0,\ 2).\\\\\text{The formula of a distance between two points:}\\\\d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\\\\text{Substitute:}\\\\d=\sqrt{(2-(-2))^2+(0-3)^2}=\sqrt{4^2+(-3)^2}=\sqrt{16+9}\\\\=\sqrt{25}=5\\\\Answer:\ \boxed{(x-3)^2+(y-(-2))^2=5^2\to\boxed{(x-3)^2+(y+2)^2=25}}$