Question

The order of differential equation of family of circles touching two given circles externally is....

Answer 1

Are there any answer choices

Answer 2

Yes they are
A)1
B)2
C)3

Answer 3

I swear this question makes no sense to me.

Answer 4

Like where's the differential equation?

Answer 5

I know right

Answer 6

And it doesnt make sence

Answer 7

That's what we need to find....

Answer 8

Actually the fact i know is that the locus of the centre of family of circles is a hyperbola...

Answer 9

Bt after this i m unable to get what to do next ...i mean how to proceed...

Answer 10

there are no derivatives involved here lol
i guess

Answer 11

what grade is this

Answer 12

12th...

Answer 13

is your profile picture you

Answer 14

@parthkohli there is obviously derivative whenever any function exists...u will study it later...:)

Answer 15

u can obtain a diff eq only after getting a family of ciecles.. eq with constants..then u keep differentiating it to remove all the constants..and u will have a diff eq

Answer 16

*circles

Answer 17

sorry i dont know

Answer 18

Do u want to say thT i shud solve it using differential of general hyperbolA ...?

Answer 19

i am not sure about the family of circles..part..did u do that part..?

Answer 20

It is definitely going to be a hyperbola ..

Answer 21

I mean the centre of those circles lie on a hyperbol

Answer 22

how did u find that out?

Answer 23

It's easy u know dis fact that hyperbola is locus of points whose difference from two fixed point is a constant quantity...

Answer 24

yeah

Answer 25

Dat's how v get it...

Answer 26

Since the two circles R fixed n we have been given that the circle touches two circles externally then u can simply say that
Let radius of circle be r n that of fixed circles be r1 n r2 then r+r1 will be the distance between the circle n C1 n similarly r+r2 will be for another circle C2

Answer 27

Noe subtract the two n we get r1-r2 which is a constant quantity...

Answer 28

@hartnn pls help...

Answer 29

i don't think i would be of much help..maybe i can help to arrive at the diff eq after u frame the family of circles eq..(even i think its a hyperbola..if thats correct for sure then the order is 2 for sure!!)

Answer 30

Yup ...even i m getting the same if we consider it to be a general hyperbola

Answer 31

Bt the ans is not matching...

Answer 32

oh..ok i'll try and let u know..

Answer 33

Fine....thanks anyways

Answer 34

hey wait!

Answer 35

Yaa ...

Answer 36

we made a mistake in thinking its a hyperbola..only the locus of the "centre" of the family of circles will be in the form of a hyperbola..right?!

Answer 37

but the are asking for the equation of the circle...

Answer 38

Yess...i know dis thing ..

Answer 39

Okk...bt what will be the equation of circle....then..

Answer 40

we have only its centre..we need radius

Answer 41

V know its centre is lying on hyperbola n wt about its radius

Answer 42

i wrote the same!!

Answer 43

How to get it now?

Answer 44

Lol...

Answer 45

lemme think..

Answer 46

K

Answer 47

U ther??

Answer 48

@parthkohli wud u like to help...

Answer 49

i didn't get any idea still..

Answer 50

It"s okk...

Answer 51

hmm..

Answer 52

so as you know the locus of center of the circle is hyperbola. (as you detailed above).
if we cosider the the center of the circle as (a,b).
than we can also write "b" as = b=>f(a) (b in terms of a.
so, r=f(a,b), r is radius here.
the equation of this circle is linear, so order of differential equation of this circle will be "1".
ok

Answer 53

How did u say r is a function of (a n b)?

Answer 54

@newtonson will u pls...tell?

Answer 55

Answer is 3

Answer 56

No