Finding Curve of Intersection

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mattnx

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Sep 5, 2009
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Hey, my math teacher assigned us this problem:

Find Curve of Intersection of 2y^2 - z^2 = 1 - x^2 - 3x and 2x^2 + 2 - 2x^2 - 6x - 5y = 0

My first thought would probably be set the two equations equal to each other, but I am at a loss at what to do next. Can anyone help?
 
Are you serious? 2x^2 - 2x^2 = 0 certainly simplifies things. Care to confirm as written or perhaps repair?
 
Is there a typo?. You have 2x^2-2x^2 in the second equation. Double check please.
 
Uh yeah I think that's right, because my teacher wrote it that way (it's handwritten). I thought it was pretty weird at first too.
 
Something seems wacky.

But, in any event, solve the second equation for y and sub into the first. This gives one equation in terms of x and z.

Then, try to solve that resulting equation for z.
 
Hey sorry to be so questioning, but why would I want to do what you said? I don't mean that in a bad way, I just wanna know why I do the steps I should do.

In any case, I solved for z, and it was sqrt(97x^2 + 27x - 17) / 5

Is that supposed to be the curve of intersection?
 
Don't solve for z. Solve for z^2 and then think about all that stuff you studied in analytic geometry.

Hint: You may wish to complete the square on the x-portion.
 
Did someone mention intersection?

Carl Sandburg - Blue Island Intersection

SIX street ends come together here.
They feed people and wagons into the center.
In and out all day horses with thoughts of nose-bags,
Men with shovels, women with baskets and baby buggies.
Six ends of streets and no sleep for them all day.
The people and wagons come and go, out and in.
Triangles of banks and drug stores watch.
The policemen whistle, the trolley cars bump:
Wheels, wheels, feet, feet, all day.

In the false dawn when the chickens blink
And the east shakes a lazy baby toe at to-morrow,
And the east fixes a pink half-eye this way,
In the time when only one milk wagon crosses
These three streets, these six street ends,
It is the sleep time and they rest.
The triangle banks and drug stores rest.
The policeman is gone, his star and gun sleep.
The owl car blutters along in a sleep-walk.
 


Double-click images, to expand.

[attachment=1:2h7cmdwc]Intersection.JPG[/attachment:2h7cmdwc][attachment=0:2h7cmdwc]Intersection2.JPG[/attachment:2h7cmdwc]
 

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And then of course....

Down to the crossroad, fell down on my knees
Down to the crossroad, fell down on my knees
Asked the Lord above "Have mercy, help poor Bob, if you please"

Mmmmm, standin' at the crossroad, well I tried to flag a ride
Standin' at the crossroad, well I tried to flag a ride
Nobody seem to know me, they just pass me by

The sun goin' down, boy, dark gon' catch me here
The sun goin' down, boy, dark gon' catch me here
I haven't got no lovin' sweet woman that love and feel my care

You can run, tell my friend-boy Willie Brown
You can run, you can run tell my friend Willie Brown
I'm standin' at the crossroad, I believe I'm sinkin' down

Lyrics to Crossroad (Robert Johnson) :
 
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