Answer:
(x+1)²+(y-5.5)²=11.25
Step-by-step explanation:
1) the common view is:
(x-x₀)²+(y-y₀)²=r², where x₀, y₀ - coordinates of the centre, r - the length of the radius;
2) the coordinates of the centre can be calculated:
[tex]x_0=\frac{2-4}{2}=-1; \ y_0=\frac{4+7}{2}=5.5.[/tex]
3) the length of the radius is:
[tex]r=\sqrt{(-1-2)^2+(5.5-4)^2}=\sqrt{11.25}.[/tex]
4) if the centre is (-1;5.5) and r²=11.25, then it is possible to make up the required equation:
(x+1)²+(y-5.5)²=11.25
