Answer:
(x-1)²+(y-3)²=65
Step-by-step explanation:
the common view of the equation of a circle is:
a) (x-a)²+(y-b)²=r², where (a;b) - the centre of the required circle, r - the radius of the required circle;
b) using the coordinates of the endpoint of the given diameter it is possible to calculate the coordinates of the centre of the required circle and its radius²:
the coordinate x of the required circle is: (9-7)/2=1;
the coordinate y of the required circle is: (2+4)/2=3.
the radius² of the required circle is:
r²=0.25*[(9- -7)²+(2-4)²]=0.25*260=65.
c) after the substitution the values of 'a'; 'b' and 'r²' into the common equation of the circle:
(x-1)²+(y-3)²=65.
PS. additional: the given points (9;2) and (-7;4) belong to the final equation, if to substitute their coordinates into it.
The suggested way of solution is not the only one.
