Question

The coordinates at the end of

the diameter of a circle are
(-2,1) and (4,3). Find the
equation of the circle.

Answer 1

Explanation:

Center of circle will be at the midpoint of (-2,1) and (4,3):

`M=((x_1+x_2)/(2) ,(y_1+y_2)/(2) )`

`=((-2+4)/(2) ,(1+3)/(2) )`

`=(1,2)`

Radius will be distance from circle center (1,2) to edge (4,3):

`r=√((y_2-y_1)^2+(x_2-x_1)^2 )`

`=√((4-1)^2+(3-2)^2 )`

`=√(3^2+1^2 )`

`=√(10)`

Equation of circle with center (1,2) and radius
`√(10)`:

`(x-h)^2+(y-k)^2=r^2` center (h,k) radius r

`(x-1)^2+(y-2)^2=√(10)^2`

`(x-1)^2+(y-2)^2=10`

SOLUTION:
`(x-1)^2+(y-2)^2=10`