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Thread: parabola and circle

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    parabola and circle

    find the points of intersection of parabola and the circle


    y=1+2x-x^2
    x^2-2x+y^2=3

    Please show step by step
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    Quote Originally Posted by skml02 View Post
    find the points of intersection of parabola and the circle


    y=1+2x-x^2
    x^2-2x+y^2=3

    Please show step by step
    (1) $\displaystyle y = 1 + 2x - x^2$

    (2) $\displaystyle 3 = x^2 - 2x + y^2$.


    Add the equations together to eliminate the $\displaystyle x$ terms.


    $\displaystyle y + 3 = 1 + y^2$

    $\displaystyle 0 = y^2 - y -2$

    $\displaystyle 0 = (y - 2)(y + 1)$

    $\displaystyle y = 2$ or $\displaystyle y = -1$.


    Substitute these values into equation (1) and solve for $\displaystyle x$.
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