## AravindG 3 years ago Can anyone give me some tricky , or conceptual questions on "tangents and normals" which i can use to teach my fellow students in a lecture tomorrow .I am equipped with ordinary questions(like finding equation of tangent and normal when function is given) but i want the students to use their brains..do help please :)

1. lgbasallote

with or without calculus?

2. AravindG

with calculus

3. moha_10

sorry what do u want exactly ?? @AravindG

4. AravindG

any suggestion ? @UnkleRhaukus , @ujjwal , @dumbcow , @Hero , @Callisto , @.Sam. , @satellite73

5. AravindG

@moha_10 i need a questions above ordinary level which are tricky and need use of "brain" on the topic "tangents and normals".As i told "I am equipped with ordinary questions(like finding equation of tangent and normal when function is given)"

6. vishweshshrimali5

Hi @AravindG you can use the study material of some coaching centres of IIT they have many such questions

7. AravindG

please share if you have :)

8. UnkleRhaukus

how many possible tangents does a triangle have?

9. AravindG

gr8 :) hmm lemme think....6?

10. UnkleRhaukus

three?

11. AravindG

are u sure ?

12. UnkleRhaukus

|dw:1346766221076:dw|

13. UnkleRhaukus

|dw:1346766232595:dw|

14. UnkleRhaukus

a tangent is just a flat side

15. AravindG

|dw:1346766337812:dw| i thought there will be these 3 also ..kk gt it bt wasnt tht question too simple?

16. UnkleRhaukus

is what sense are those tangents?

17. AravindG

i thought if we where asked to draw tangents at vertices we draw like that

18. hartnn

aren't tangents suppose to touch the curve only in one point ? @UnkleRhaukus

19. UnkleRhaukus

tangent are ment to approximate the cure as flat

20. AravindG

@UnkleRhaukus can u think of better qns (involving calculs) ?

21. UnkleRhaukus

do we usually define the normal as pointing out from the curve or in ? are there two normals to a flat line?

22. AravindG

u see there are a few students who just byheart the formula and appy it mechanically .. i want to teach them why using brain is important

23. UnkleRhaukus

i dont remember the formula at all,

24. UnkleRhaukus

isn's it just the derivative?

25. AravindG

nt formula i mean mechanical proces like finding f'(x) then using slope point form get to eqn of tangent and normal

26. AravindG

i need to get qns which are one steap ahead(which require use of brain") of these usual qns (bt focusing on the same idea )

27. UnkleRhaukus

in three dimensions the tangent is a plane right/?

28. AravindG

think so ..i am nt sure

29. UnkleRhaukus

30. AravindG

tangent is same as function

31. UnkleRhaukus

hmm

32. hartnn

maybe u can give a equation of a circle and ask them to find the equation of tangent passing through (a,b) where (a,b) is either center or inner point of a circle...they would not be able to find slope only.........

33. AravindG

@hartnn that seems a good idea

34. AravindG

need more such qns

35. mukushla

Find all values of a for which 2 curves\[y=ax^2+ax+1\]\[x=ay^2+ay+1\]are tangent to each other.

36. AravindG

@mukushla cooooooool!!!!

37. .Sam.

38. .Sam.

@mukushla I think if y=ax^2+ax+1 x=2ay+1 will be workable, changed the y^2 to y

39. mukushla

yeah this involves lesser steps...

40. mathmate

@AravindG Is your class working in 2-d or 3-d?

41. AravindG

2d

42. mathmate

Try: Find the shortest distance between two curves f1(x) and f2(x). Example: f1(x)=x^2, and f2(x)=2(x-1)^2+4

43. AravindG

where do we bring in tangents in that?

44. mathmate

This is not an easy problem, because the tangents have to be parallel, but at different values of x on each curve. They would minimize the distance after that.

45. .Sam.

@AravindG are my 4 questions good enough?

46. AravindG

@.Sam.do u have the answers ?

47. .Sam.

yeah

48. AravindG

post it pls

49. AravindG

yeah ur qns are very useful thx

50. .Sam.

51. AravindG

thx a lot!!!!

52. .Sam.

welcome :)