Shaks 2 years ago Show that the equation represents a circle by rewriting it in standard form, and find the center and radius of the circle. x2 + y2 + 4y + 2 = 0

1. Shaks

Show that the equation represents a circle by rewriting it in standard form, and find the center and radius of the circle. x2 + y2 + 4y + 2 = 0

2. Shaks

can u helpme

3. saifoo.khan

@Directrix are you good with circles?

4. Shaks

noup

5. Shaks

help mee

6. Shaks

sir

7. Shaks

helloo

8. Directrix

@Shaks I'm hoping you understand the process of completing the square. We'll need that to get x2 + y2 + 4y + 2 = 0 into the standard form of the equation of a circle. That standard form is (x - h) ^2 + (y - k) ^2 = r^2 where (h,k) are the coordinates of the center of the circle and r is the radius of the circle. Check out the attachment.

9. Shaks

is that the asnwer

10. Directrix

No. Focus on the process, not the answer.

11. Shaks

yeaa

12. Shaks

getting it kind it

13. Shaks

of

14. Shaks

The center is (0,-2)

15. Directrix

So, x^2 + y^2 + 4y + 2 = 0 can be written as x^2 + y^2 + 4y + __4_ = 0 + 4 (x + 0) ^2 + (y + 2) ^2 = 4 ---> Your Circle Now, look at the standard form for the circle equation, compare it to the equation, and pick out the coordinates of the center and the value of the radius. Post what you get, and I'll check. @Shaks

16. Directrix

r = ?

17. Shaks

x^2+(y+2)^2=3 is this the standerd form

18. Shaks

r= -2

19. Shaks

hello

20. Shaks

are u there

21. Directrix

r= -2 --> Incorrect

22. Shaks

then how to solve it

23. Directrix

Look at standard form for circle equation: That standard form is (x - h) ^2 + (y - k) ^2 = r^2 where (h,k) are the coordinates of the center of the circle and r is the radius of the circle. What positive number times itself = 4? That's your r.

24. Shaks

2 is r

25. Directrix

Correct.

26. Shaks

got it

27. Shaks

noo r is not 2

28. Shaks

is it 4

29. Directrix

@Shaks I messed up by dropping the 2. So, x^2 + y^2 + 4y + 2 = 0 can be written as x^2 + y^2 + 4y + __4_ = 2 + 4 = 6. r^2 = 6 and r is square root of 6.

30. Shaks

is it 6

31. Shaks

2.44

32. Directrix

6 = r^2. We want r which is square root of 3.

33. Shaks

hmm

34. Shaks

trying to understand

35. Shaks

1.7

36. Shaks

did not get it it too doficult

37. Shaks

difficult

38. Directrix

You approximated square root of 3 to get 1.7. I stick with exact form but I don't know what your options are.

39. Shaks

yaa i got it

40. Shaks

Find all real solutions of the equation. (Enter your answers as a comma-separated list. If there is no real solution, enter NO REAL SOLUTION.) x + 42 = x

41. Shaks

now 1 more sum