Find the standard form of the equation of the circle with endpoints of a diameter at the points (9,2) and (-7.4).

(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.

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