anonymous one year ago Which of these points lies on a circle centered at A(3, 3) and passing through B(6, 5)? C(1, 6) D(6, 0) E (0, 3) F(3, -1) G(3, 6)

1. FireKat97

I think the easiest way to approach this, would be firstly to apply the distance formula between A and B (since B lies on the circle and is not the centre, it must lie on the circumference) so by finding this distance, we can determine the radius

2. FireKat97

do you remember the distance formula?

3. anonymous

$2pr ^{2}$

4. FireKat97

not quite, thats the circumference formula, we want the distance between two points

5. FireKat97

so the equation you want to use is $d = \sqrt{(y - y1)^2 + (x - x1)^2}$

6. anonymous

oh yea

7. FireKat97

yup, so apply that and tell me what you get for the distance

8. anonymous

3.6

9. anonymous

@FireKat97

10. FireKat97

yup, thats correct! but as a general rule, when we get square roots and stuff, you're better off keeping your answer in exact form, so just stick with √13

11. FireKat97

btw do you remember what the general equation of a circle is?

12. anonymous

not really

13. FireKat97

okay so the general equation of a circle is- (x - {x coordinate of centre})^2 + (y - {y coordinate of centre})^2 = radius^2

14. FireKat97

and we have been given the centre, and had recently worked out the radius, so try subbing in the info we now have, and show me what you get

15. anonymous

2.32?

16. FireKat97

umm, not exactly, so we sub in the stuff we now know to get, (x - 3)^2 + (y - 3)^2 = (√13)^2 so (x - 3)^2 + (y - 3)^2 = 13 do you follow?

17. anonymous

yes

18. FireKat97

okay, so now we can try subbing the points given as options into our equation, to see which coordinates satisfy it.

19. anonymous

(1,6)

20. FireKat97

Yup! Thats correct!

21. anonymous

thankyou!

22. FireKat97

no problem :)