# analytical geometry

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the points M(6,-8) and E(8,6) are on a circle with radius 10 units. Determine the equation of the line equidistant from points M and E

• analytical geometry -

what does the circle have to do with it?

The midpoint of ME is (7,-1)
The slope of ME is 14/2 = 7

The slope of the perpendicular bisector of ME is thus -1/7

The line is thus
(y+1)/(x-7) = -1/7
y = -x/7

Makes sense, since the circle is x^2 + y^2 = 100, and the perpendicular bisector of ME must pass through the center of the circle, or (0,0).

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