Question

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 :)

Answer 1

with or without calculus?

Answer 2

with calculus

Answer 3

sorry what do u want exactly ?? @AravindG

Answer 4

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

Answer 5

@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)"

Answer 6

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

Answer 7

please share if you have :)

Answer 8

how many possible tangents does a triangle have?

Answer 9

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

Answer 10

three?

Answer 11

are u sure ?

Answer 12

a tangent is just a flat side

Answer 13

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

Answer 14

is what sense are those tangents?

Answer 15

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

Answer 16

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

Answer 17

tangent are ment to approximate the cure as flat

Answer 18

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

Answer 19

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

Answer 20

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

Answer 21

i dont remember the formula at all,

Answer 22

isn's it just the derivative?

Answer 23

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

Answer 24

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 )

Answer 25

in three dimensions the tangent is a plane right/?

Answer 26

think so ..i am nt sure

Answer 27

what about one dimension ?

Answer 28

tangent is same as function

Answer 29

hmm

Answer 30

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.........

Answer 31

@hartnn that seems a good idea

Answer 32

need more such qns

Answer 33

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

Answer 34

@mukushla cooooooool!!!!

Answer 35

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

Answer 36

yeah this involves lesser steps...

Answer 37

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

Answer 38

2d

Answer 39

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

Answer 40

where do we bring in tangents in that?

Answer 41

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.

Answer 42

@AravindG are my 4 questions good enough?

Answer 43

@.Sam.do u have the answers ?

Answer 44

yeah

Answer 45

post it pls

Answer 46

yeah ur qns are very useful thx

Answer 47

thx a lot!!!!

Answer 48

welcome :)