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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 :)

Mathematics
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with or without calculus?
with calculus
sorry what do u want exactly ?? @AravindG

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Other answers:

any suggestion ? @UnkleRhaukus , @ujjwal , @dumbcow , @Hero , @Callisto , @.Sam. , @satellite73
@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)"
Hi @AravindG you can use the study material of some coaching centres of IIT they have many such questions
please share if you have :)
how many possible tangents does a triangle have?
gr8 :) hmm lemme think....6?
three?
are u sure ?
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a tangent is just a flat side
|dw:1346766337812:dw| i thought there will be these 3 also ..kk gt it bt wasnt tht question too simple?
is what sense are those tangents?
i thought if we where asked to draw tangents at vertices we draw like that
aren't tangents suppose to touch the curve only in one point ? @UnkleRhaukus
tangent are ment to approximate the cure as flat
@UnkleRhaukus can u think of better qns (involving calculs) ?
do we usually define the normal as pointing out from the curve or in ? are there two normals to a flat line?
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
i dont remember the formula at all,
isn's it just the derivative?
nt formula i mean mechanical proces like finding f'(x) then using slope point form get to eqn of tangent and normal
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 )
in three dimensions the tangent is a plane right/?
think so ..i am nt sure
what about one dimension ?
tangent is same as function
hmm
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.........
@hartnn that seems a good idea
need more such qns
Find all values of a for which 2 curves\[y=ax^2+ax+1\]\[x=ay^2+ay+1\]are tangent to each other.
@mukushla cooooooool!!!!
@mukushla I think if y=ax^2+ax+1 x=2ay+1 will be workable, changed the y^2 to y
yeah this involves lesser steps...
@AravindG Is your class working in 2-d or 3-d?
2d
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
where do we bring in tangents in that?
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.
@AravindG are my 4 questions good enough?
@.Sam.do u have the answers ?
yeah
post it pls
yeah ur qns are very useful thx
thx a lot!!!!
welcome :)

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