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Conic Sections Test - 3

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Conic Sections Test - 3
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    The line y = m x + c is a normal to the circle x2 + y2 + 2gx + 2fy + c = 0 if

    Solution

    x2 + y2 + 2gx + 2fy + c = 0 has center (-g,-f)

    As normal passes through center so center will satisfy the equation of normal

    put y=-f and x=-g in equation of the line y=mx+c

    -f = m(-g) +c

    which gives mg =f+c.

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