## zuha one year ago A circle has an area of approximately 78.5 square units. If the center of the circle is at (2,4). Which of the following points is on the circle?

1. Zuha

(-6, 4) (2, -1) (-4, -4) (2, -9)

2. Nnesha

do you know the standard form equation of the circle ?

3. Zuha

Do you mean the distance?

4. Nnesha

yes same equation for both

5. Zuha

Yyeah, I can't understand how to calculate that, I do know the d formula tho ;v;

6. Nnesha

well the standard form equation of the circle is $\huge\rm (x-h)^2 +(y-k)=r^2$ where (h,k) is the center and r = radius

7. Nnesha

use the formula area of a circle $\huge\rm A= \pi r^2$ to find r (radius )

8. Zuha

is (y-k) also supposed to be ^2? So is h=2 and k=4??

9. Nnesha

yes right forgot sorry about that $\huge\rm (x-h)^2 +(y-k)^2=r^2$

10. Nnesha

yes right h=2 k =4

11. Zuha

And I should just try each of the options until one of them is 78.5...?

12. Zuha

@Nnesha ?

13. Nnesha

thanks for tag i was afk alright first you need to find the radius

14. Nnesha

the given is 78.5 area so substitute a for 78.5 and then solve for r

15. Zuha

a?

16. Nnesha

what do you mean ?

17. Nnesha

use the formula area of a circle $\huge\rm A= \pi r^2$ to find radius

18. Zuha

Oohhhh 78.5=pir^2 Umm, I assume I divide pi from both sides then?

19. Nnesha

yes right

20. Zuha

25 o.o

21. Zuha

So I do 3.14*25^2?

22. Nnesha

yes r^2 equal 25 yes right forgot sorry about that $\huge\rm (x-2)^2 +(y-4)^2=25$ now you can substitute (x,y) for each order pair if you get equal sides then that order pair would be the answer

23. Nnesha

no we need r^2 which is 25 you can check your work 3.14*25^2 iif its equal 78.5 then 25 is correct

24. Zuha

It isn't equal to 78.5 .-.

25. Nnesha

r^2 =25 not r= so dont' take square of 25

26. Nnesha

$\huge\rm \frac{ 78.5 }{ 5 }=r^2 ~~~~----> 25=r^2$ to find r you should take square root but we need r^2 for the equation

27. Zuha

Ooh Okay, then yeah it's right--so then I just try each of the answers in the slots for x and y until I get the right one?

28. Nnesha

yep!

29. Zuha

Oh okay! I already know the correct answer which is (2,-1) and I tested it and it's right! Thanks so much!! :)

30. Nnesha

np :=)goood work!