Intersection of TWO QUADRICS/Conics

[glueball8]

Homework Statement

Find all the plane (x,y) all points of intersection of two quadric:
2x^2-xy+3y^2=36,
3x^2-4xy+5y^2=36

Homework Equations

The Attempt at a Solution

I want to know the general process to solve something like this. Is the problem solved by using det somehow? Or divide by y^2 and let k=x/y then make 2 equations are solve that somehow??

 

[glueball8]

Basiclly this, http://math.stackexchange.com/questions/261945/finding-intersections-of-two-quadrics.

But I don't know how he got " So I just tried taking the difference of the two quadrics (which is essentially the case of k=−1) and solved directly as so and got {(4,2),(−4,−2),(3,3),(−3,−3)} as my intersection points."

How did he solved directly?

 

[glueball8]

OK, so eq 2-eq1, then use that as eq 3. Solve eq1 and eq3 as a system, which got that answer. Is this process correct?

My class is a ring&field class. I don't see how this even related at all... No determinate needed to solve this?

 

[tiny-tim]

hi glueball8!

(try using the X² button just above the Reply box )

OK, so eq 2-eq1, then use that as eq 3. Solve eq1 and eq3 as a system, which got that answer.

yes, that will give you two values for x/y, which you can then substitute into the original equations

(and if they weren't both 36 on the RHS, of course you would multiply one of them to make the RHSs the same)

 

[glueball8]

hi glueball8!

(try using the X² button just above the Reply box )yes, that will give you two values for x/y, which you can then substitute into the original equations

(and if they weren't both 36 on the RHS, of course you would multiply one of them to make the RHSs the same)

Thanks, do you know what does this have to do with ring&fields (Abstract algebra)? I thought you had to use something special to solve it but apparently its just regular system of equations.

 

[tiny-tim]

Thanks, do you know what does this have to do with ring&fields (Abstract algebra)?

i've no idea

anyone? ​