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If the two curves 2x^2+kxy+y^2+2x+4y+1=0...

If the two curves `2x^2+kxy+y^2+2x+4y+1=0` and `x^2+4xy+4y^2-x+2y+4=0` intersect at 4 non concyclic points then k=

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`S=2x^2+kxy+y^2+2x+4y+1=0`
`P=x^2+4xy+4y^2-x+2y+4=0`
Equation of circle
`S+lambdaP=0`
`2x^22+kxy+y^2+2xy+4y+1+lambdax^2+4lambdaxy+4lambday^2-lambdax=0`
`(2+lambda)X^2+(k+4lambda)xy+(1+4lambda)y^2+(2-lambda)x+(4+2lambda)y=0`
coeff of `x^2`=cosff of `y^2`
coeff of xy=0
...
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