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- Homework Statement:
- Find the intersection/system of equation between a parabola and circle

- Relevant Equations:
- x^2+xy+y^2=18; x^2+y^2=12

Given:

x^2+xy+y^2=18

x^2+y^2=12

Attempt:

(x^2+y^2)+xy=18

12+xy=18

xy=6

y^2=12-x^2

(12)+xy=18

xy=6

Attempt 2:

xy=6

x=y/6

y^2/36+(y/6)y+y^2=18

43/36y^2=18

y ≠ root(6) <- should be the answer

Edit:

Just realized you cant plug the modified equation back into its original self

I plugged y=6/x into the circle instead and got:

x^2+36/x^2=12

now I have x^4+36=12x^2

x^4-12x^2+36=0

x^2+xy+y^2=18

x^2+y^2=12

Attempt:

(x^2+y^2)+xy=18

12+xy=18

xy=6

y^2=12-x^2

(12)+xy=18

xy=6

Attempt 2:

xy=6

x=y/6

y^2/36+(y/6)y+y^2=18

43/36y^2=18

y ≠ root(6) <- should be the answer

Edit:

Just realized you cant plug the modified equation back into its original self

I plugged y=6/x into the circle instead and got:

x^2+36/x^2=12

now I have x^4+36=12x^2

x^4-12x^2+36=0

Last edited: