## anonymous one year ago The equation of a circle is in the form x^2 +y^2 +Cx+Dy+E=. Find an equation of the circle shown in the illustration by determining C,D, and E

1. Michele_Laino

2. anonymous

|dw:1444143802955:dw|

3. Michele_Laino

here as we can see the center of your circumference is at point $$(3,0)$$

4. Michele_Laino

sorry, we have to replace the coordinates of the points you provided, into your generic equation

5. anonymous

How? I'm so confused

6. Michele_Laino

for examnple, your circumference passes at point $$(0,0)$$ so I replace $$x=0,y=0$$ into your equation, so I get this: ${0^2} + {0^2} + C \cdot 0 + D \cdot 0 + E = 0$ what is $$E$$?

7. anonymous

Even plug in the points (3,3) and (6,0)?

8. Michele_Laino

that's right!

9. anonymous

okay thank you so much

10. Michele_Laino

:)

11. anonymous

Wait @Michele_Laino

12. anonymous

I have to write and solve a system of three equations in the three unknowns C, D, and E. Then write the equation of the circle in general form:

13. anonymous

wait @Michele_Laino

14. Michele_Laino

yes! correct! As you can see we have an algebraic system with 2 unknowns, since we have already determined E as $$E=0$$

15. anonymous

But don't we have to come up with 3 systems

16. Michele_Laino

if we replace $$x=3,y=3$$ into your equation,we get: 9+9+3C+3D=0 that is the first equation of our system, the first one is E=0

17. Michele_Laino

if we replace $$x=6,y=0$$, we get: 36+0+6C+0.D=0 that is the third equation

18. Michele_Laino

please solve those new equations with respect to C and D