help with coordinate geo qs (1 Viewer)

[Smeegen999]

hi

i'm reviewing the coord. geometry topic and i need help with this qs:

Find the coordinates of the centre of a circle that passes through the points:
(7,2)
(2,3)
(-4,-1)

could anyone explain 2 me how I would attempt this qs?

anyhelp would be great. thanks!!

 

[Mark576]

(x-h)² + (y-k)² = r² (1) is the general equation of the circle. Substitute the first point into the general form (1):
(7-h)² + (2-k)² = r²
=> 49 - 14h + h² + 4 - 4k + k² = r²
=> 53 - 14h - 4k + h² + k² = r² (2)
And the second point:
(2-h)² + (3-k)² = r²
4 - 4h + h² + 9 - 6k + k² = r²
=> 13 - 4h - 6k + h² + k² = r² (3)
And the third point:
(-4-h)² + (-1-k)² = r²
=> 16 + 8h + h² + 1 + 2k + k² = r²
=> 17 + 8h + 2k + h² + k² = r² (4)
(2) - (3) gives:
5h - k = 20 (4)
And (4) - (3) gives:
3h + 2k = -1 (5)
h = 3, k = -5
So the centre of the circle is (3,-5)!

 

[Smeegen999]

thankyou!