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solve the system

7x^2 - 5y^2 + 20y = 3
21x^2 + 5y^2 =209

  • math -

    since 7x^2 = 5y^2 - 20y + 3

    21x^2 = 15y^2 - 60y + 9

    plug that into the 2nd equation to get

    20y^2 - 60y - 200 = 0
    y^2 - 3y - 10 = 0
    (y-5)(y+2) = 0

    From there you can see that the circle and the hyperbola intersect at

    (3,-2) (-3,-2) (2,5) (-2,5)

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