## anonymous one year ago Derive the equation of the parabola with a focus at (0, −4) and a directrix of y = 4. f(x) = −16x2 f(x) = 16x2 f(x) = −one sixteenth x2 f(x) = one sixteenthx2

1. anonymous

@satellite73 @princeharryyy

2. anonymous

@pooja195

3. anonymous

Ans: f(x) = (-1/16)*(x²) D.

4. anonymous

how did you get that ?

5. anonymous

@WhateverYouSay

6. anonymous

If the focus is at (0,-4) and the directrix is y = 4 then the vertex of the parabola is midway between these two features at (0,0). The parabola is thus a downward opening parabola with the standard equation x² = 4cy where c is the distance from the vertex to the focus. In this question, c = -4.

7. anonymous

is that the formula that you would use for all parabola equations?

8. anonymous

@nono266 can you explain this better?

9. anonymous

@ganeshie8

10. anonymous

well it say's it's the standard equation. So i am assuming yes...

11. anonymous

how do you know which one is 'C'

12. princeharryyy

still need help!

13. princeharryyy

??? @scenemunster

14. anonymous

15. princeharryyy

ok! from the start.

16. princeharryyy

should we?

17. anonymous

yes how do you do that?

18. princeharryyy

The parabola can look like

19. princeharryyy

|dw:1438718841051:dw|

20. princeharryyy

can u see that. @scenemunster

21. princeharryyy

and please if u are interested in learning u must be interactive. or u can just have answers. @scenemunster It's up to you.

22. anonymous

yes

23. anonymous

i understand

24. princeharryyy

let's take a general form. suppose this figure.

25. princeharryyy

|dw:1438719011601:dw|

26. anonymous

this amkes no sense to me tbh

27. anonymous

makes

28. princeharryyy

now, In this figure Point B is known as the vertex of the parabola, A is known as the focus, and line D is known as Directrix of the parabola.

29. princeharryyy

where C is at the same distance from origin as is the focus of parabola.

30. princeharryyy

has, it started making sense @scenemunster

31. anonymous

yes

32. princeharryyy

great, The general equation of east facing parabola, whose vertex is at (0,0) is y^2 = 4ax

33. princeharryyy

are you getting it.

34. princeharryyy

where a is the distance from vertex to the focus of the parabola

35. anonymous

so (a,o)?

36. princeharryyy

as distance being a, and the for every positive x there will be two values of y one negative and the other positive , the parabola is sketched this way. i.e., east facing.

37. anonymous

im so confused

38. princeharryyy

where

39. princeharryyy

?

40. anonymous

the east facing parabola

41. princeharryyy

|dw:1438719685600:dw|

42. princeharryyy

TAKING THIS AS CONVENTION, ARE U COMFORTABLE NOW.

43. princeharryyy

@scenemunster ??? please be quick! I don't have much time.

44. anonymous

ok so a =4?

45. princeharryyy

4 comes in general equation. they made the general equation this way

46. princeharryyy

a is some constant which changes it's value according to question.

47. anonymous

@amistre64 can you help as well. im sorry im naturally blonde and i dont know XD

48. anonymous

so what is the equation like how do i set it up

49. princeharryyy

Ok, leave that.

50. princeharryyy

51. princeharryyy

let me make the figure.

52. princeharryyy

|dw:1438720085660:dw|

53. princeharryyy

where a =-4. y = -16x^2

54. princeharryyy

focus of parabola (0,-4)

55. princeharryyy

That means the answer is a

56. princeharryyy

@scenemunster

57. anonymous

ok. i understand but y would it be a my guess was d

58. princeharryyy

wait a second, it won't actually be A or D it would be C, reason, general equation, x^2 = -4by => x^2 = -16y, b=4 =>y =-x^2/16

59. anonymous

ok. my besty said the same thing

60. princeharryyy

@scenemunster , n sorry actually I was explaining the east one so by mistake I told u A earlier.

61. princeharryyy

and, later we changed the direction of parabola to south and hence the equation changed. Sorry 'bout that but the answer is C for 100%

62. princeharryyy

@scenemunster

63. anonymous

ok i got it thank you

64. princeharryyy

yw :)