## anonymous one year ago Find an equation of the circle shown below. (x + 10)2 + (y − 10)2 = 289 (x − 10)2 + (y − 10)2 = 289 (x − 10)2 + (y + 10)2 = 289 (x − 10)2 + (y − 10)2 = 17

1. anonymous

2. anonymous

Ok. So to find the equation of a circle we need TWO things: the center of the circle and the radius

3. anonymous

okay how would we find those?

4. anonymous

Since they did not give us the center, we have to use the midpoint formula. They also didn't give us the distance of the radius. We have to use the Distance formula. Ok so let's do this step by step

5. anonymous

The mid-point formula is $\left( \frac{ x _{2} + x _{1} }{ 2 }, \frac{ y _{2} + y _{1} }{ 2 } \right)$

6. anonymous

Basically find the average of both x values and both y values from the coordinates given in order to determine the center of the circle

7. anonymous

Try to plug in those x and y values into the formula, and then tell me what you got.

8. anonymous

$\frac{ 18+2 }{ 2 },\frac{ 25+(-5) }{ 2 }$okay so for the midpoint we would have this?

9. anonymous

which would be 10,10 right?

10. anonymous

@happyrosy sorry i had to leave

11. anonymous

okay so then the distance formula is $\sqrt{(x2-x1)^{2}+(y2-y1)^{2}}$

12. anonymous

so then i plug them in which would be $\sqrt{(18-2)^{2}+(25-(-5))^{2}}$

13. anonymous

so that would lead to $\sqrt{(16)^{2}+(30)^{2}}$

14. anonymous

so we would then have $\sqrt{256+900}$

15. anonymous

so the square root of 1156 wich would be 34

16. anonymous

so 34 is the distance?

17. anonymous

(x-h)^2 + (y-k)^2 =r^2

18. anonymous

(x-10)^2 + (y-10)^2 = 1156

19. anonymous

okay i messed up with the radius but i think i got the distance right

20. anonymous

im going to go with (x − 10)2 + (y − 10)2 = 289

21. anonymous

the 34 you got was the diameter. Half of 34 is 17, which would be the radius. Square the 17, equaling to 289. So, yes your final is correct. GREAT JOB ON THE WORK!!

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