## anonymous one year ago Does anyone know how to do this? Circle O, with center (x, y), passes through the points A(0, 0), B(–3, 0), and C(1, 2). Find the coordinates of the center of the circle.

1. campbell_st

use the distance formula as the distance from any point on the circumference is always equal so OA = Ob = OC this will give the equation or locus or the circle you'll then need to factor it to a standard form

2. triciaal

|dw:1436990750032:dw|

3. triciaal

center (0,0) |dw:1436990958298:dw|

4. triciaal

equation of a circle with center (0,0) x^2 + y^2 = r^2 where r is the radius in this sketch the radius is OR

5. triciaal

|dw:1436991295757:dw|

6. triciaal

one approach is to plot the points first then as above also given by @campbell_st find OA, OB and OC same as OR in the sketch solve for (x,y)

7. triciaal

do you see how to do it now?

8. anonymous

I hate to ask but Do you guys know the answer, I mean I would do it but I just wanna finish this homeschool already

9. triciaal

I would have to do the problem

10. campbell_st

if you use the distance formula OA = OB then $\sqrt{(x - 0)^2 + (y - 0)^2} = \sqrt{(x + 3)^2 + (y - 0)^2}$ so this becomes $x^2 + y^2 = x^2 + 6x + 9 + y^2$ this will allow you to solve for x. to get y use the distance between OA and OC $\sqrt{(x - 0)^2 + (y - 0)^x} = \sqrt{(x -1)^2+(y - 2)^2}$ which becomes $x^2 + y^2 = (x -1)^2 + (y -2)^2$ substitute the answer for x that you got in the previous calculation then solve for y

11. campbell_st

well I have an answer, and the centre contains fractional values for x and y

12. triciaal

13. anonymous

|dw:1437175931767:dw|

14. triciaal

|dw:1436992391537:dw|

15. anonymous

I found an answer for x which is -1.5 but the answer I got for y is 1/4(5-2x)

16. anonymous

Is that correct

17. triciaal

|dw:1436992999048:dw|

18. triciaal

sorry have to leave

19. anonymous

Its okay Ill figure out the y part

20. triciaal

|dw:1437015241447:dw|

21. triciaal

center (x, y) = (-3/2, 1/2)

22. triciaal

yes what you have for y is incomplete substitute the value for x