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 :)

- AravindG

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- lgbasallote

with or without calculus?

- AravindG

with calculus

- anonymous

sorry what do u want exactly ?? @AravindG

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- AravindG

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

- 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)"

- vishweshshrimali5

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

- AravindG

please share if you have :)

- UnkleRhaukus

how many possible tangents does a triangle have?

- AravindG

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

- UnkleRhaukus

three?

- AravindG

are u sure ?

- UnkleRhaukus

|dw:1346766221076:dw|

- UnkleRhaukus

|dw:1346766232595:dw|

- UnkleRhaukus

a tangent is just a flat side

- AravindG

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

- UnkleRhaukus

is what sense are those tangents?

- AravindG

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

- hartnn

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

- UnkleRhaukus

tangent are ment to approximate the cure as flat

- AravindG

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

- UnkleRhaukus

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

- 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

- UnkleRhaukus

i dont remember the formula at all,

- UnkleRhaukus

isn's it just the derivative?

- AravindG

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

- 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 )

- UnkleRhaukus

in three dimensions the tangent is a plane right/?

- AravindG

think so ..i am nt sure

- UnkleRhaukus

what about one dimension ?

- AravindG

tangent is same as function

- UnkleRhaukus

hmm

- 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.........

- AravindG

@hartnn that seems a good idea

- AravindG

need more such qns

- anonymous

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

- AravindG

@mukushla cooooooool!!!!

- .Sam.

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

- anonymous

yeah this involves lesser steps...

- mathmate

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

- AravindG

2d

- 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

- AravindG

where do we bring in tangents in that?

- 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.

- .Sam.

@AravindG are my 4 questions good enough?

- AravindG

@.Sam.do u have the answers ?

- .Sam.

yeah

- AravindG

post it pls

- AravindG

yeah ur qns are very useful thx

- AravindG

thx a lot!!!!

- .Sam.

welcome :)

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