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    So the question is "A tangent to the cirlce has gradient -1. Find 2 points at which it could touch the circle and hence 2 possible equtions for the tangent"
    I've already got the centre (2,2), radius (root 8) and the equation of the circle which is (x-2)^2+(y-2)^2=8
    Any ideas how to do this?
    thanks in advance

    If a tangent to a circle at a point has gradient of -1. So the equation of the tangent is of the form  y=-x+c for some constant c.
    Now if you plug this expression for y into the equation of the circle, it forms a quadratic equation. You can then consider that the discriminant of this quadratic equation will be 0 since the line is tangent to the circle.
    You find c (2 values) from this and then it is straight forward to find the two points where these lines intersect the circle.
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Updated: November 8, 2016

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