## IsTim 3 years ago Determine the equation of the tangent to the curve at a given point. x^2+9y^2=37 (1,2)

1. IsTim

I've gotten the slope of -1/18, but I don't know if that's correct. And if so, how do I continue?

2. IsTim

So, first, dy/dx=-x/dy. I then subbed in (1,2) and got -1/18.

Lol uhh so I cant give answers so ill just leave now but what youv done so far is correct :D

4. IsTim

I don't need the answer. I need to know what my process afterwards should be.

5. inkyvoyd

What's the derivative?

6. inkyvoyd

7. IsTim

1. Derivative is 2x+18y(dy/dx)=0. Right? 2. I figured that out already...

lol ink I can give him an answer ;D

9. inkyvoyd

x^2+9y^2=37 dy/dx 37=dy/dx x^2+dy/dx 9y^2 0=2x+18y dy/dx

10. inkyvoyd

No, you won't give him the answer he's looking for. THe answer he's looking for is an explanation, because, as everyone knows, it's the explanantion that matters in calc

11. IsTim

I already have the answer in my textbook and potentially Wolfram Alpha. I need to know how to GET there though.

12. inkyvoyd

Normally at this point I try to isolate dy/dx for convenience

13. shruti

from conic section?

14. inkyvoyd

0=2x+18y dy/dx (-2x)/(18y)=dy/dx x/(-9y)=dy/dx

15. IsTim

Yeah, I think I did that.It's -x/dy right? @ Shruti: I don't think so...

16. inkyvoyd

17. inkyvoyd

Although my work here is moot, because i'm in 9th grade.

18. IsTim

Ok. Thanks for the help so far.

19. IsTim

Ok. How would I get to the answer of x+18y-37=0 from knowing that the slope is -1/18?

20. inkyvoyd

eh?

21. inkyvoyd

If you had the derivative and wanted to get the original equation?

22. IsTim

I guess?

23. IsTim

@shruti By conics did you mean http://www.purplemath.com/modules/circle3.htm

24. amistre64

since this is an equation of an ellipse, y can be considered an implicit function of x right?

25. IsTim

I guess. My notes only reveal the steps. This work is not from a textbook.

26. IsTim

In fact, it's not even addressed in my textbook. That's strange.

27. amistre64

it can be .... to derive implicitly, ignore the form of the variable and treat everything as tho it acted like you normally think of deriving x^2+9y^2=37 ; just derive it all, but dont toss out the derived bits 2x x' + 18y y' = 0 now lets consider this when we derive it with respect to x x' = dx/dx = 1 y' = dy/dx like normal so, lets solve it for y'

28. inkyvoyd

If you have the derivative, and want to get the original equation, you take the anti-derivative of it

29. inkyvoyd

30. inkyvoyd

Otherwise, I might have to look into it.

31. IsTim

Y' is -x/dy, which, when we sub in (1,2) is -1/18 right?

32. dpaInc

yes tim, -1/18 is right

33. IsTim

What would I do next then?

34. inkyvoyd

Well, you have a point, and a slope.

35. inkyvoyd

(1,2) -> point -1/18 -> slope

36. inkyvoyd

remember, y=mx+b

37. IsTim

Would I sub those into y=mx+b?

38. dpaInc

you have slope, you have a point, put it in point slope form...

39. inkyvoyd

put in the point and the slope, and then you have b

40. inkyvoyd

then, put in y=mx+b, cept don't put in that point

41. inkyvoyd

This isn't a calculus problem, this is an algebra problem, :D

42. IsTim

Sorry, what is point slope form? It's algebra? I must really have been "dumbing" down these years...

43. inkyvoyd

Ok.

44. inkyvoyd

There's multiple ways of writing the equation for a line.

45. inkyvoyd

This is point slope: y-y1=m(x-x1)

46. inkyvoyd

this is slope intecept: y=mx+b

47. inkyvoyd

This is standard form: ax+by=c

48. inkyvoyd

I normally work with slope intercept, because i'm more used to it.

49. inkyvoyd

However, point slope is the fastest way to go here.

50. inkyvoyd

y-y1=m(x-x1) (x1,y1)=(1,2) m=-1/18

51. IsTim

The answer is in the form of ax+by=c I guess, but I am also more familiar with slope intercept.

52. IsTim

Wait, I already have the slope... I know it is -1/18. But how do I get to x+18y-37?

53. inkyvoyd

y-1=(-1/18)(x-2) now, just isolate y, and distribute x

54. inkyvoyd

They have given you the point that the line must pass through, and you have found the slope,

55. IsTim

Oh. I finally understand. Thank you very much. I will call out again if I need help.

56. inkyvoyd

Ok. :D

57. IsTim

Wait, 1 and 2 in y-1=(-1/18)(x-2)/ Shouldn't it be y-2=(-1/18)(x-1)? Because (1,2)?

58. inkyvoyd

Yes

59. inkyvoyd

I got it confused myself. xD

60. IsTim

Why doesn't my answer look like that provided on the sheet, which is x+18y-37?

61. IsTim

Oh. I figured that out. Sorry.

62. IsTim

Thank you all for putting forth the effort to assist me.

63. IsTim

Or at the very least, looking over the question.

64. inkyvoyd

No problem :)

65. inkyvoyd

This is good premptive practice for me ;)

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