Question

Help me please:

Answer 1

Let e1 and e2 denote the eccentricites of the hyperbolas
\[\frac{ x^2 }{ m^2 }-\frac{ y^2 }{ n^2 }=1 \]
and
\[\frac{ y^2 }{ n^2 }-\frac{ x^2 }{ m^2 }=1\]
respectively.
Verify that
\[e \left(\begin{matrix}2 \\ 1\end{matrix}\right)e \left(\begin{matrix}2 \\ 2\end{matrix}\right)=e \left(\begin{matrix}2 \\ 1\end{matrix}\right)+e \left(\begin{matrix}2 \\ 2\end{matrix}\right)\]

Answer 2

@triciaal

Answer 3

@wio

Answer 4

not current on this, sorry

Answer 5

can you tag someone who might know?

Answer 6

@satellite73, @mathstudent55, @jim_thompson5910 can you please help?

Answer 7

by the way its "e sub 1 squared" incase you were confused

Answer 8

@pico33 ?

Answer 9

and eccentricity is basically c/a

Answer 10

@jhannybean do you mind helping?

Answer 11

@ganeshie8

Answer 12

@Abhisar

Answer 13

@dan815

Answer 14

@Compassionate

Answer 15

@ganeshie8 will you please help

Answer 16

its actually
\[e_1^2e_2^2=e_1^2+e_2^2\]

Answer 17

not the other one i inserted

Answer 18

Not sure about these..

Answer 19

do you know anyone who would know? and if you do can you tag them please?

Answer 20

draw what eccentricities are

Answer 21

isnt it c/a?

Answer 22

whats c and a

Answer 23

im trying to decide whether a is m or n

Answer 24

c is \[\sqrt{m^2+n^2}\]

Answer 25

ok

Answer 26

you should google what eccentricities of hyprbole are

Answer 27

what do you mean google it? isnt it just c/a?

Answer 28

so like \[\frac{ m }{ \sqrt{m^2+n^2} }\]

Answer 29

@wio

Answer 30

ok

Answer 31

but is that e1 or e2?

Answer 32

lets say its e1, what is e2?

Answer 33

n^2 over that number?

Answer 34

so there is no way of knowing if "m" is "a" or "b"?

Answer 35

there is

Answer 36

how?

Answer 37

if u learn what eccentricities are :P

Answer 38

im jk

Answer 39

can you help me?

Answer 40

its ok

Answer 41

but i think c/a
c=the hyptenues of the major and miinor length

Answer 42

and a= probably the major

Answer 43

isnt c the distance from the center to the vertex?

Answer 44

yeah that is equivalent to the hyp of m and n

Answer 45

eccentricity tells u how curved or close to parallel the hyperbola is

Answer 46

so then how would you know which is "a" and "b"?

Answer 47

okay so think which one wud matter

Answer 48

say u have x^2/a^2-y^2/b^2=1 parabola

Answer 49

can u graph that

Answer 50

\[e_1 = \frac{c}{a} = \dfrac{\sqrt{m^2+n^2}}{m}\]

\[e_2 = \frac{c}{a} = \dfrac{\sqrt{m^2+n^2}}{n}\]

Answer 51

i dont remember how :(

Answer 52

plug them in the given equation and do ur algebra