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  1. #1
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    circle

    determine the coordinates of the centre and the radius of the circle with equation: $\displaystyle 2x^2 + 2y^2 - 16x + 4y = 1$

    i started by making it $\displaystyle 2[x^2 - 8x + (-4)^2] + 2[y^2 + 2y + (1)^2] = 1 + (-8)^2 + (2)^2$ and then

    $\displaystyle 2(x - 4)^2 + 2(y + 1)^2 = \sqrt69$ and i said the coordinates are $\displaystyle (8, -1)$ and the radius $\displaystyle \sqrt69$

    the book says the radius is $\displaystyle \frac {1}{2} \sqrt70$ and the coordinates are $\displaystyle (4, -1)$

    can someone tell me how i'm wrong please? thankyou
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  2. #2
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    Quote Originally Posted by mark View Post
    determine the coordinates of the centre and the radius of the circle with equation: $\displaystyle 2x^2 + 2y^2 - 16x + 4y = 1$

    i started by making it $\displaystyle 2[x^2 - 8x + (-4)^2] + 2[y^2 + 2y + (1)^2] = 1 + (-8)^2 + (2)^2$ and then

    $\displaystyle 2(x - 4)^2 + 2(y + 1)^2 = \sqrt69$ and i said the coordinates are $\displaystyle (8, -1)$ and the radius $\displaystyle \sqrt69$

    the book says the radius is $\displaystyle \frac {1}{2} \sqrt70$ and the coordinates are $\displaystyle (4, -1)$

    can someone tell me how i'm wrong please? thankyou
    $\displaystyle
    2x^2 + 2y^2 - 16x + 4y = 1
    $

    $\displaystyle 2(x^2+y^2-8x+2y) = 1$

    $\displaystyle (x^2+y^2-8x+2y) = \frac{1}{2}$

    $\displaystyle (x-4)^2 - 16 + (y+1)^2-1 = \frac{1}{2}$

    $\displaystyle (x-4)^2 + (y+1)^2 = \frac{33}{2}
    $

    Centre is $\displaystyle (4,-1)$ and radius is $\displaystyle \sqrt{\frac{33}{2}}$

    Not sure where $\displaystyle \frac{1}{2} \,\sqrt{70}$ comes from
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  3. #3
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    isn't it $\displaystyle \sqrt\frac{35}{2}$?
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  4. #4
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    Quote Originally Posted by mark View Post
    isn't it $\displaystyle \sqrt\frac{35}{2}$?
    A simple typo.
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