## julie001 3 years ago Circle S has an equation of (x – 16)2 + (y + 9)2 = 4. What is the center and radius of circle S?

1. sugargurl

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2. ash2326

A circle with center ( a, b ) and radius r has equation given as \[(x-a)^2+(y-b)^2=r^2\] We are given equation of circle as \[(x – 16)^2 + (y + 9)^2 = 4\] @julie001 Can you compare the two equations to find the center and radius?

3. julie001

4. julie001

im not sure

5. ash2326

6. ash2326

@julie001 where you have doubt?

7. julie001

comparintg the equations

8. sugargurl

9. julie001

hoW ?

10. Mertsj

No sugargurl. Answer is NOT the second choice.

11. ash2326

Work step by step \[(x-a)^2=(x-16)^2\] so a=16 Now you could find b and r, using the same procedure

12. sugargurl

YUO THE ANSWER IS THE 3RD CHOICE THANKS FOR CORRECTING ME @ MERTSJ

13. julie001

@ash2326 im still lost

14. ash2326

Did you understand how I found a?

15. julie001

from the question ?

16. ash2326

Yeah, standard equation of a circle is \[(x-a)^2+(y-b)^2=r^2\] and the equation given in the question is \[(x-16)^2+(y+9)^2=4\] We need to find the center (a, b) and radius r. So we compare the two equations \[(x-a)^2=(x-16)^2\] To make both sides equal a should be 16, so a=16 Now can you find b, by comparing \[(y-b)^2=(y+9)^2\]

17. julie001

so its Center: (16, -9); Radius: 2

18. ash2326

Could you show me your work?

19. Mertsj

There is no work to show. We know that if the equation is written in the form: \[(x-h)^2+(y-k)^2=r^2\] then the center is (h,k) and the radius is r

20. julie001

i just plugged in the numbers with the equation

21. Mertsj

So write the given equation: \[(x-16)^2+(y-(-9))^2=2^2\] and it is immediately obvious that the center is (16,-9) and the radius is 2

22. julie001

@Mertsj is it Center: (16, -9); Radius: 2

23. Mertsj

and it is immediately obvious that the center is (16,-9) and the radius is 2

24. julie001

thanks !

25. Mertsj

yw