- #1
threetheoreom
- 43
- 0
when there is enough block ... here is my problem.
a hyperbola having F(-5,0) and D(5,0) and difference of focal radii 6.
We can use |PF - PD|= 6 or PF - PF = [tex]\pm[/tex]6.
I apply the distance formula ..eleminate radicals and simplify.
I get
16X^2 -9y^2=144
Divinding both sides by 144 I get
The hyperbolic equation
(x^2/9)-(y^2/16) = 1
analysing to graph ( herein lie the problems )
First determining the intercepts ..it is easy to see the intercepts on the x-axis are 3 and -3 ( verified by makeing y 0 in the above equ.) and that making x 0 we can aslo varify that there arn't any y intercepts (-y^2/16)
( that I understand)
The book goes on to say to determine the extent of the graph
making for y we get y=[tex]\pm[/tex]4/3 [square root] of x^2 -9 and
x = [tex]\pm[/tex] 3/4 [squre root] of y^2 + 16
y is real if and only if |x| >= 3 thus no part of the graph lies between -3 and 3 ... in the second x is real for all y variables [tex]\Leftarrow[/tex] someone explain that please.
this part is killing me, they said notice that y = [tex]\pm[/tex]4/3 [square root] x^2 - 9 = [tex]\pm[/tex]4/3x [square root] 1-9/x^2 . [tex]\Leftarrow[/tex] I don't get this I'm thinking they factored it and i should be able to see that of course i tried ..but i can't see how . [ block]
they the go on to say that as the absolute value of x gets larger the square root of 1- 9/x^2 get closer to 1 and therefore |x| gets larger the graphapproaches the lines y [tex]\approx[/tex][tex]\pm[/tex] 4/3x. thus as
|x| becomes larger the graph approaches the lines y= 4/3x and -3/4x. :grumpy:
Thanks guys
Orson
p.s sorry for the bad tex
a hyperbola having F(-5,0) and D(5,0) and difference of focal radii 6.
We can use |PF - PD|= 6 or PF - PF = [tex]\pm[/tex]6.
I apply the distance formula ..eleminate radicals and simplify.
I get
16X^2 -9y^2=144
Divinding both sides by 144 I get
The hyperbolic equation
(x^2/9)-(y^2/16) = 1
analysing to graph ( herein lie the problems )
First determining the intercepts ..it is easy to see the intercepts on the x-axis are 3 and -3 ( verified by makeing y 0 in the above equ.) and that making x 0 we can aslo varify that there arn't any y intercepts (-y^2/16)
( that I understand)
The book goes on to say to determine the extent of the graph
making for y we get y=[tex]\pm[/tex]4/3 [square root] of x^2 -9 and
x = [tex]\pm[/tex] 3/4 [squre root] of y^2 + 16
y is real if and only if |x| >= 3 thus no part of the graph lies between -3 and 3 ... in the second x is real for all y variables [tex]\Leftarrow[/tex] someone explain that please.
this part is killing me, they said notice that y = [tex]\pm[/tex]4/3 [square root] x^2 - 9 = [tex]\pm[/tex]4/3x [square root] 1-9/x^2 . [tex]\Leftarrow[/tex] I don't get this I'm thinking they factored it and i should be able to see that of course i tried ..but i can't see how . [ block]
they the go on to say that as the absolute value of x gets larger the square root of 1- 9/x^2 get closer to 1 and therefore |x| gets larger the graphapproaches the lines y [tex]\approx[/tex][tex]\pm[/tex] 4/3x. thus as
|x| becomes larger the graph approaches the lines y= 4/3x and -3/4x. :grumpy:
Thanks guys
Orson
p.s sorry for the bad tex
Last edited: