AravindG
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 :)
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lgbasallote
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with or without calculus?
AravindG
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with calculus
moha_10
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sorry what do u want exactly ?? @AravindG
AravindG
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any suggestion ? @UnkleRhaukus , @ujjwal , @dumbcow , @Hero , @Callisto , @.Sam. , @satellite73
AravindG
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@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
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Hi @AravindG you can use the study material of some coaching centres of IIT they have many such questions
AravindG
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please share if you have :)
UnkleRhaukus
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how many possible tangents does a triangle have?
AravindG
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gr8 :) hmm lemme think....6?
UnkleRhaukus
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three?
AravindG
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are u sure ?
UnkleRhaukus
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|dw:1346766221076:dw|
UnkleRhaukus
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|dw:1346766232595:dw|
UnkleRhaukus
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a tangent is just a flat side
AravindG
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|dw:1346766337812:dw| i thought there will be these 3 also ..kk gt it bt wasnt tht question too simple?
UnkleRhaukus
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is what sense are those tangents?
AravindG
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i thought if we where asked to draw tangents at vertices we draw like that
hartnn
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aren't tangents suppose to touch the curve only in one point ? @UnkleRhaukus
UnkleRhaukus
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tangent are ment to approximate the cure as flat
AravindG
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@UnkleRhaukus can u think of better qns (involving calculs) ?
UnkleRhaukus
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do we usually define the normal as pointing out from the curve or in ?
are there two normals to a flat line?
AravindG
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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
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i dont remember the formula at all,
UnkleRhaukus
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isn's it just the derivative?
AravindG
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nt formula i mean mechanical proces like finding f'(x)
then using slope point form get to eqn of tangent and normal
AravindG
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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
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in three dimensions the tangent is a plane right/?
AravindG
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think so ..i am nt sure
UnkleRhaukus
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what about one dimension ?
AravindG
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tangent is same as function
UnkleRhaukus
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hmm
hartnn
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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
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@hartnn that seems a good idea
AravindG
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need more such qns
mukushla
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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
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@mukushla cooooooool!!!!
.Sam.
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.Sam.
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@mukushla I think if
y=ax^2+ax+1
x=2ay+1
will be workable, changed the y^2 to y
mukushla
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yeah this involves lesser steps...
mathmate
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@AravindG Is your class working in 2-d or 3-d?
AravindG
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2d
mathmate
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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
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where do we bring in tangents in that?
mathmate
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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.
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@AravindG are my 4 questions good enough?
AravindG
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@.Sam.do u have the answers ?
.Sam.
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yeah
AravindG
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post it pls
AravindG
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yeah ur qns are very useful thx
.Sam.
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AravindG
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thx a lot!!!!
.Sam.
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welcome :)