## anonymous 5 years ago The center of the circle that passes through the points (-2,3), (0,-3), and (4,-3) is________ a) (2,2) b) there is not enough data to find the center c) (1,2) d) (2,1)

1. anonymous

first we can find the eq of circle passing through three points, then can check the centre

2. anonymous

how do I do that?

3. anonymous

general eq of the circle is $x^2+y^2+2gx+2fy+c=0$

4. anonymous

substitute the three points in this eq we get three eqs in three unknows find the unknows g,f and c

5. anonymous

centre is $\sqrt{g^2+f^2-c}$

6. anonymous

for(-2,3) 4+9-4g+6f+c=0

7. anonymous

for(0,-3) 9-6f+c=0

8. anonymous

for(4,-3) 16+9+8g-6f+c=0

9. anonymous

-4g+6f+c=-13 -6f+c=-9 8g-6f+c=-25

10. anonymous

subtracting 1 n 3 -12g+12f=12 -g+f=1

11. anonymous

sub 1 n 2 -4g+12f=-4 g-3f=1

12. anonymous

adding the resultant eqs -2f=2 f=-1 which gives g=-2 n c=-3

13. anonymous

center=(-g,-f)=(2,1)

14. anonymous

so D is the right option:)

15. anonymous

m sorry the formula i wrote earlier is to find the radius

16. anonymous

17. anonymous

u got all the lenghy computations?

18. anonymous

lengthy*

19. anonymous

for the most part

20. anonymous

what do g and f represent though?

21. anonymous

if there is some confusion, u can ask:)

22. anonymous

these r constants

23. anonymous

the eq i wrote is the general eq of the circle

24. anonymous

finding out g,f and c, we can find the eq of the circle

25. anonymous

okay thank you

26. anonymous

welcome:)