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Find the locus of the foot of the perpendicular dropped from a focus onto a variable tangent of the hyperbola 16y² - 9x² = 1.

1. x² + y² = 1/9
2. x² + y² = 9
3. x² + y² = 7/144
4. x² + y² = 1/16

Correct answer: x² + y² = 1/9

Solution

The pedal curve of the foot of the perpendicular from a focus on a tangent is the auxiliary circle x² + y² = (semi-transverse axis)²; here that radius squared is 1/9.

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