# Coordinate Geometry - circle question! One end of a diameter of a circle with equation `x^2 + y^2 - 4x + 4y = 2` is (3,1)... One end of a diameter of a circle with equation `x^2 + y^2 - 4x + 4y = 2` is (3,1). Find the coordinates of the other end of the diameter.     I did a similar question that required to find the equation of the tangent to the circle with a equation given a point, which I firstly found the centre and found the slope of the tangent by making it negative reciprocal. I understand that type of question, but I am having trougble with this one. Help!

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Lix Lemjay | Certified Educator

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`x^2 + y^2 - 4x + 4y = 2`

Express the equation in standard form `(x-h)^2 + (y-k)^2 = r^2` to be able to find the center of the circle.

`(x^2 - 4x) + (y^2 + 4y) = 2`

Perform completing the square method.

`(x^2 - 4x + 4) + (y^2 + 4y + 4) = 2 + 4 + 4`

`(x-2)(x-2) + (y+2)(y+2) = 10`

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