Find the locus of the foot of the perpendicular drawn from the center upon any tangent to the ellipse $\frac{x ^{2}}{a ^{2}} + \frac{y ^{2}}{b ^{2}} = 1 .$

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Find the locus of the foot of the perpendicular drawn from the center upon any tangent to the ellipse

\frac{x ^{2}}{a ^{2}} + \frac{y ^{2}}{b ^{2}} = 1 .

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Question Text

Find the locus of the foot of the perpendicular drawn from the center upon any tangent to the ellipse

\frac{x ^{2}}{a ^{2}} + \frac{y ^{2}}{b ^{2}} = 1 .

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