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Math Help - geometric and quadratic equations

  1. #1
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    geometric and quadratic equations

    The line x + y - 1 = 0 intersects the circle x^2 + y^2 = 13 at A(x1,y1) and B(x2, y2). Without finding the coordinates of A and B, find the length of the chord AB.

    HINT: form a quadratic equation in x and evaluate l x1 - x2 l and l y1 - y2 l

    thanks

    how do i got about doing this question
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  2. #2
    Senior Member Stroodle's Avatar
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    If you solve these equations simultaneously you get x_1=-2 and x_2=3 , so \left |x_1-x_2\right |=5

    and y_1=3 and y_2=-2 so \left |y_1-y_2\right |=5

    Now using Pythagorus' Theorem you have C=\sqrt{5^2+5^2}

    So the length of the chord is 5\sqrt{10} units
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