Answer:
(x+1)²+(y-5.5)²=45/4.
Step-by-step explanation:
1) the common form of the required equation is: (x-a)²+(y-b)²=r², where 'a' and 'b' are the coordinates of the centre of the given circle, r - radius of the given circle.
2) the midpoint of the diameter is the centre of the given circle, its coordinates are:
[tex]\frac{2-4}{2}=-1; \ and \ \frac{4+7}{2}=5.5.[/tex]
3) the length of the radius of the given circle is:
[tex]r=\frac{1}{2}*\sqrt{(2+4)^2+(4-7)^2)}=\sqrt{\frac{45}{4}}.[/tex]
4) according to the common form and calculated the centre O(-1;5.5) and the radius it is possible to make up the required equation of the circle:
[tex](x+1)^2+(y-5.5)^2=\frac{45}{4}.[/tex]
