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Math Help - [SOLVED] eqn of circle

  1. #1
    Member helloying's Avatar
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    [SOLVED] eqn of circle

    Given that a circle with centre(-1.5,0.5)and radius 5/2(√ 2)
    Find the length of the chord 4x-3y-5=0 of the circle.

    Thanks
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  2. #2
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    Quote Originally Posted by helloying View Post
    Given that a circle with centre(-1.5,0.5)and radius 5/2(√ 2)
    Find the length of the chord 4x-3y-5=0 of the circle.

    Thanks
    Plug in the given values into the general equation of a circle:

    \left(x+\frac32\right)^2+\left(y-\frac12 \right)^2=\dfrac{25}2

    Solve the equation of the line for y = \frac43x-\frac53

    Plug in the term of y into the equation of the circle. Solve the equation for x. You'll get 2 values: x_1 = 2~\vee~x_2 = -1

    Plug in these values into the equation of the line to get the corresponding values of y: y_1 = 1~\vee~y_2 = -3

    The line intersects the circle in the points P(2, 1) and Q(-1, -3).

    Calculate the length of the chord PQ:

    |\overline{PQ}|=\sqrt{(2-(-1))^2+(1-(-3))^2} = 5
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