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Let S-=x^2+y^2+2gx+2f y+c= be a given ci...

Let `S-=x^2+y^2+2gx+2f y+c=` be a given circle. Find the locus of the foot of the perpendicular drawn from the origin upon any chord of S which subtends a right angle at the origin.

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To find the locus of the foot of the perpendicular drawn from the origin to any chord of the circle \( S: x^2 + y^2 + 2gx + 2fy + c = 0 \) which subtends a right angle at the origin, we can follow these steps: ### Step 1: Write the equation of the circle The given equation of the circle is: \[ x^2 + y^2 + 2gx + 2fy + c = 0 \] ...
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