Write the equation of a circle in standard form with diameter stack A B with bar on top. Where A(7, 5) and B(-1, -1). For full credit, show your work.

ANSWER[tex]{(x - 3)}^{2} + {(y - 2)}^{2} = 25[/tex]EXPLANATIONThe given circle has diameter A(7,5) and B(-1,-1).The center of the circle is the midpoint of the diameter.The midpoint is given by the formula:[tex] (\frac{x_1+x_2}{2} , \frac{y_1+y_2}{2} )[/tex]We substitute the points to get[tex](\frac{7+ - 1}{2} , \frac{5+ - 1}{2} )[/tex][tex](3 , 2 )[/tex]The radius of the circle is calculated using the center and any point on the circle.[tex]r = \sqrt{ {(x_2-x_1)}^{2} + {(y_2-y_1)}^{2} } [/tex][tex]r = \sqrt{ {(3- - 1)}^{2} + {(2 - - 1)}^{2} } [/tex][tex]r = \sqrt{16 + 9 } [/tex][tex]r = \sqrt{25} = 5[/tex]We substitute the center and the radius into the standard equation of the circle.[tex] {(x - h)}^{2} + {(y - k)}^{2} = {r}^{2} [/tex]Substitute the values to get,[tex] {(x - 3)}^{2} + {(y - 2)}^{2} = {5}^{2} [/tex][tex]{(x - 3)}^{2} + {(y - 2)}^{2} = 25[/tex]